antalya algebra days xvii85.111.17.208/nvetkinlik/events/2015_aad/acg.pdf · 2017. 3. 2. ·...
TRANSCRIPT
Antalya Algebra Days XVII
20 - 24 May, 2015
Sirince - Izmir - Turkey
TMD (Turkish Mathematical Society), TMD-MAD and MimarSinan Fine Arts University have contributed financial support to
the conference. We thank all institutions.
Contents
Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
I Invited Speakers 3Laurence Barker . . . . . . . . . . . . . . . . . . . . . . . 5Alexandre Borovik . . . . . . . . . . . . . . . . . . . . . . 6Inna Capdeboscq . . . . . . . . . . . . . . . . . . . . . . . 6Giovanni Falcone . . . . . . . . . . . . . . . . . . . . . . . 7Ehud Hrushovski . . . . . . . . . . . . . . . . . . . . . . . 8Anargyros Katsampekis . . . . . . . . . . . . . . . . . . . 8Otto Kegel . . . . . . . . . . . . . . . . . . . . . . . . . . 9Ekin Ozman . . . . . . . . . . . . . . . . . . . . . . . . . . 9Peter Plaumann . . . . . . . . . . . . . . . . . . . . . . . 9Serge Randriambololona . . . . . . . . . . . . . . . . . . . 10Donna M. Testerman . . . . . . . . . . . . . . . . . . . . . 11Simon Thomas . . . . . . . . . . . . . . . . . . . . . . . . 12Apostolos Thoma . . . . . . . . . . . . . . . . . . . . . . . 12Sukru Yalcınkaya . . . . . . . . . . . . . . . . . . . . . . . 13Hamza Yesilyurt . . . . . . . . . . . . . . . . . . . . . . . 14
II Contributed Talks 15Evrim Akalan . . . . . . . . . . . . . . . . . . . . . . . . . 17Yıldırım Akbal . . . . . . . . . . . . . . . . . . . . . . . . 17Emine Albas . . . . . . . . . . . . . . . . . . . . . . . . . 18Mustafa Kemal Berktas . . . . . . . . . . . . . . . . . . . 19Tuba Cakmak . . . . . . . . . . . . . . . . . . . . . . . . . 20Cafer Calıskan . . . . . . . . . . . . . . . . . . . . . . . . 20
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Yusuf Danısman . . . . . . . . . . . . . . . . . . . . . . . 21Ismail Demir . . . . . . . . . . . . . . . . . . . . . . . . . 22M. Pınar Eroglu . . . . . . . . . . . . . . . . . . . . . . . 22Sehmus Fındık . . . . . . . . . . . . . . . . . . . . . . . . 23Betul Gezer . . . . . . . . . . . . . . . . . . . . . . . . . . 24Kubra Gul . . . . . . . . . . . . . . . . . . . . . . . . . . 25Ahmet Muhtar Guloglu . . . . . . . . . . . . . . . . . . . 25Noomen Jarboui . . . . . . . . . . . . . . . . . . . . . . . 26Shizuo Kajı . . . . . . . . . . . . . . . . . . . . . . . . . . 26Faruk Karaaslan . . . . . . . . . . . . . . . . . . . . . . . 28Emrullah Kırklar . . . . . . . . . . . . . . . . . . . . . . . 28Piotr Kowalski . . . . . . . . . . . . . . . . . . . . . . . . 29Kagan Kursungoz . . . . . . . . . . . . . . . . . . . . . . 29Omer Kusmus . . . . . . . . . . . . . . . . . . . . . . . . 30Ugur Odabası . . . . . . . . . . . . . . . . . . . . . . . . . 31Belgin Ozer . . . . . . . . . . . . . . . . . . . . . . . . . . 32Zeynep Ozkurt . . . . . . . . . . . . . . . . . . . . . . . . 32Nurhan Sokmez . . . . . . . . . . . . . . . . . . . . . . . . 33Mesut Sahin . . . . . . . . . . . . . . . . . . . . . . . . . . 35Murat Sahin . . . . . . . . . . . . . . . . . . . . . . . . . 35Elif Tan . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Vladimir Tolstykh . . . . . . . . . . . . . . . . . . . . . . 37Ugur Ustaoglu . . . . . . . . . . . . . . . . . . . . . . . . 38Cetin Urtis . . . . . . . . . . . . . . . . . . . . . . . . . . 39David Bradley-Williams . . . . . . . . . . . . . . . . . . . 39Tugba Yıldırım . . . . . . . . . . . . . . . . . . . . . . . . 40Yousef Zamani . . . . . . . . . . . . . . . . . . . . . . . . 40
III Posters 43Cigdem Bicer . . . . . . . . . . . . . . . . . . . . . . . . . 45Hilal Donmez . . . . . . . . . . . . . . . . . . . . . . . . . 45Serdar Enginoglu . . . . . . . . . . . . . . . . . . . . . . . 46Zekiye Eser . . . . . . . . . . . . . . . . . . . . . . . . . . 47Tugce Guler, Ummahan Acar, Emre Ciftlikli . . . . . . . 51Nil Mansuroglu . . . . . . . . . . . . . . . . . . . . . . . . 51L. de O. Miranda, L. O. de Miranda, L. B. B. Miranda . . 52Celil Nebiyev . . . . . . . . . . . . . . . . . . . . . . . . . 52Engin Ozkan, Ipek Altun, Ali Aykut Gocer . . . . . . . . 54
Aslıhan Sezgin Sezer . . . . . . . . . . . . . . . . . . . . . 56Sebnem Yıldız . . . . . . . . . . . . . . . . . . . . . . . . 56Semih Yılmaz . . . . . . . . . . . . . . . . . . . . . . . . . 57
IV Participants and Committees 59Participants . . . . . . . . . . . . . . . . . . . . . . . . . . 61Committees . . . . . . . . . . . . . . . . . . . . . . . . . . 67
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Program
Wednesday, 20 May08.00-09.00: Breakfast09.00-10.00: Registration10.00-11.00: Otto Kegel11.00-11.30: Coffee break11.30-12.30: Simon Thomas12.30-14.00: Lunch14.00-15.00: Laurence Barker15.10-16.10: Giovanni Falcone16.10-16.40: Coffee break16.40-17.40: Sukru Yalcınkaya18.00: Reception
Thursday, 21 May08.00-09.00: Breakfast09.30-10.30: Peter Plaumann10.40-11.40: Inna Capdeboscq11.40-12.10: Coffee break12.10-13.10: Hamza Yesilyurt13.10-14.30: Lunch14.30-16.30: Parallel talks16.30-17.00: Coffee break17.00-19.00: Parallel talks19.00-20.00: Dinner20.30-21.30: Poster session
Friday, 22 May08.00-09.00: Breakfast09.30-10.30: Alexandre Borovik10.30-11.00: Coffee break11.00-12.00: Anargyros Katsampekis12.00-13.30: Lunch13.30: Excursion19.00-20.00: Dinner
Saturday, 23 May08.00-09.00: Breakfast09.30-10.30: Donna Testerman10.40-11.40: Apostolos Thoma11.40-12.10: Coffee break12.10-13.10: Serge Randriambololona13.10-14.30: Lunch14.30-16.30: Parallel talks16.30-17.00: Coffee break17.00-19.00: Parallel talks19.00-20.00: Dinner20.30-21.30: Alexandre Borovik
Sunday, 24 May08.00-09.00: Breakfast09.30-10.30: Ehud Hrushovski10.30-11.00: Coffee break11.00-12.00: Ekin Ozman12.00-13.00: Lunch
Part I
Invited Speakers
3
5
Blocks of Mackey categories
Laurence Barker
The biset category is an abstraction of the notions of induction,restriction, deflation and inflation. Many structures that appearin finite group representation theory, such as representation rings,Burnside rings and group cohomology, can be regarded as functorsdefined on the biset category.
For a suitable small category F of homomorphisms betweenfinite groups, we introduce two subcategories of the biset cate-gory, namely, the deflation Mackey category M←
F and the inflationMackey category M→
F . Let G be the subcategory of F consisting ofthe injective homomorphisms. We shall show that, for a field K ofcharacteristic zero, the K-linear category
KMG = KM←G = KM→
G
has a semisimplicity property and, in particular, every block ofKMG owns a unique simple functor up to isomorphism. On theother hand, we shall show that, when F is equivalent to the cate-gory of finite groups, the K-linear categories KM←
F and KM→F each
have a unique block.Our approach will be to introduce the notion of the extended
quiver algebra of a linear category. Functors on the linear categorybecome modules of the extended quiver algebra. Blocks of the lin-ear category are blocks of the extended quiver algebra. We shallprove that every block of KM←
F or KM→F is a central idempotent
of KMG . Finding the blocks is a matter of finding out how cen-tral idempotents of KMG fuse under commutation relations comingfrom deflation or inflation.
Bilkent Universitesi
6
Black box groups: back to basics
Alexandre Borovik
Black box group theory is a branch of computational group the-ory devoted to probabilistic algorithms for finite groups. We see it apart of a wider black box algebra, which deals also with finite rings,fields, projective spaces, etc. – but accepts that homomorhisms canbe trap-door functions or otherwise encrypted.
The talk will explain some basics of this new approach to blackbox groups and fields that brings them back into the realm of com-puter science and cryptography – where they have originated in1980-s in the pioneering works by Laci Babai, Endre Szemeredi,and Arjen Lenstra.
This is a joint work with Sukru Yalcınkaya.
University of Manchester
Kac-Moody groups: generation and presentations
Inna Capdeboscq
In this talk we will discuss the generation of minimal and topo-logical Kac-Moody groups, and the presentation of their compactsubgroups. The second part of the talk is based on a joint workwith A.Lubotzky and B.Remy.
The University of Warwick
7
Derivations of nilpotent Lie algebraof type {n, 2} or {2n, 1, 1}
Giovanni Falcone
Different definitions of types of a nilpotent Lie algebra have beengiven. M. Vergne gave in [6] the following one: the type {p1, . . . , pc}of a nilpotent Lie algebra h with descending central series h(i) =[h, h(i−1)] is defined by the integers pi equal to the dimension ofh(i−1)/h(i).
Notice that a Heisenberg Lie algebras has type {n, 1}, and thatnilpotent Lie algebras of type {n, 2} and {n, 1, 1} can be thoroghlydescribed ([5], [1]).
According to [3], a classification of nilpotent Lie algebras of type{n, 3} etc. can hardly be reached. A possible way of broadening thefamilies of Lie algebras of type {n, 2} and {n, 1, 1} appears thereforethat of considering their derivations.
It is interesting that in some cases these can be effectively de-scribed ([4], [2]). At the same time, cases where a description is tooinvolved appear.
References[1] C. Bartolone, A. Di Bartolo and G. Falcone, Nilpotent Lie algebras with2-dimensional commutator ideals, Linear Algebra Appl. 434 (2011), 650-656.[2] C. Bartolone, A. Di Bartolo and G. Falcone, Solvable extensions of nilpotentcomplex Lie algebras of type {2n, 1, 1}, submitted.[3] G. Belitskii, R. Lipyanski and V. V. Sergeichuk, Problems of classifyingassociative or Lie algebras and triples of symmetric or skew-symmetric matricesare wild, Linear Algebra Appl. 407 (2005), 249-262.
[4] G. Falcone and A. Figula, The action of a compact Lie group on nilpotentLie algebras of type {n, 2}, Forum Math. (to appear)[5] M. A. Gauger, On the classification of metabelian Lie algebras, Trans. Amer.Math. Soc. 179 (1973), 293-329.
[6] M. Vergne, Cohomologie des algebres de Lie nilpotentes. Application a
l’etude de la variete des algebres de Lie nilpotentes, Bull. Soc. Math. France
98 (1970), 81-116.
Universita di Palermo
8
Proper intersections in pseudo-finite structures
Ehud Hrushovski
I will discuss pseudo-finite dimensions, and present a lemma onproperness of intersections. Both old results on totally categoricalstrongly minimal sets, and more recent results of Tao on expansion,can be interpreted from this viewpoint.
Hebrew University
[email protected], [email protected]
An indispensable classification of monomialcurves in A4(K)
Anargyros Katsampekis
We give a new classification of monomial curves in the affine 4-dimensional space A4(K). It relies on the detection of those binomi-als and monomials that have to appear in every system of binomialgenerators of the defining ideal of the monomial curve; these specialbinomials and monomials are called indispensable in the literature.This way to proceed has the advantage of producing a natural nec-essary and sufficient condition for the defining ideal of a monomialcurve in A4(K) to have a unique minimal system of binomial gen-erators.
Mimar Sinan Guzel Sanatlar Universitesi
9
Large groups
Otto Kegel
We offer an interpretation of the word LARGE in the contextof group theory combining structural size with complete control of“small” groups (homogeneity).
This is a report of joint work with Mahmut Kuzucuoglu.
Bad reduction of genus three curveswith complex multiplication
Ekin Ozman
Let C be a smooth, absolutely irreducible genus 3 curve over anumber field M. Suppose that the Jacobian of C has complex multi-plication by a sextic CM-field K. Suppose further that K contains noimaginary quadratic subfield. We give a bound on the primes p ofM such that the stable reduction of C at p contains three irreduciblecomponents of genus 1.
This is a joint work with Bouw, Cooley, Lauter, Garcia, Manesand Newton.
Bogazici Universitesi
Herstein automorphisms of Moufang loops
Peter Plaumann
Let (M,µ) be a magma, that is a set M with a map
µ : M ×M → M.
We call a mapping
η : M → M
an Herstein homomorphism of (M,µ) if for x, y ∈ M one of theequations
(xy)η = xηyη or (xy)η = yηxη
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holds. If the multiplication µ is associative this concept was used inring theory (Jacobson, Rickaert, Herstein) und has some importancefor Jordan algebras. For groups Scott has shown, using the namehalf-automorphism, that such a mapping is either a homomophismor a anti-homomorphism.
K. Johnson and M. Guiliani have initiated the study of Her-stein automorphisms for loops. Later M. Giuliani and S. Gagolaproved fundamental facts of Herstein automorphisms of finite Mo-ufang loops. A. Grishkov, M. Giuliani, M. Rasskazova and L.Sabininashowed that Scott’s theorem holds for finite automorphic Moufangloops. The same result is valid for free loops in the variety of auto-morphic Moufang loops (A. Grishkov, P. Plaumann, M. Rasskazova,L. Sabinina).
In this talks I will speak in some detail about these results andwill give the necessary definitions from the Theory of Loops. Be-sides I will discuss joint work with L.Sabinia presenting a finite leftautomorphic Moufang loop of order 16, a code loop connected withthe algebra of octonions, admitting proper Herstein automorphisms.
FAU Erlangen-NurnbergUniversidad Autonma Benito Juarez de Oaxaca
Some (non-)elimination results forcomplex algebraic curves
Serge Randriambololona
A subset of Cn is said to be constructible if it can be describedby a finite boolean combination of conditions of the form
Pi(z1, · · · , zn) = 0 or Pi(z1, · · · , zn) = 0,
for some complex polynomials Pi. Similarly, a subset of Rn is saidto be semialgebraic if it can be described by a finite boolean combi-nation of conditions of the form Qj (x1, · · · , xn) ≥ 0, for some realpolynomials Qj .
Both the field of complex numbers and the ordered field of realnumbers admit quantifier elimination; that is, the projection on Cn
(respectively Rn) of a constructible (resp. semialgebraic) subset ofCn×Cm (resp. Rn×Rm) is itself constructible (resp. semialgebraic).
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In a joint work with Sergei Starchenko, we studied what happensin this projection process if the polynomials involved in the descrip-tion of the constructible set (resp. semialgebraic set) each onlyinvolves at most two different variables (depending on the polyno-mial). In the real case, the projection can again be described bypolynomials each involving at most two variables; this however failsto be true in the complex case. The difference of behaviour betweenthe real and the complex case illustrates the richness of the groupof automorphisms of C fixing Q.
Galatasaray Universitesi
Semisimple groups: subgroup structure andrepresentation theory
Donna M. Testerman
A major achievement of 20th century mathematics was Cheval-ley’s classification of the semisimple linear algebraic groups definedover an algebraically closed field. This remarkable result shows thatsuch groups are determined up to isomorphism by a set of combi-natorial data, and the list of isomorphism classes is independent ofthe characteristic of the field of definition.
In the years following this classification, many mathematicians,including Borel, Tits, Springer, and Steinberg, contributed to thefurther study of these objects, establishing results on their repre-sentation theory, endomorphisms, conjugacy classes, and quotientspaces, and further revealed the important connection between thesemisimple linear algebraic groups defined over fields of positivecharacteristic and the finite groups of Lie type, the latter of whichgive rise to the majority of the finite simple groups.
Since the late 20th century, additional effort has been made tofurther the knowledge of the subgroup structure of the semisim-ple linear algebraic groups and their finite analogues. Fundamentalreduction theorems of Aschbacher and Liebeck-Seitz have made evi-dent the link between the subgroup structure and some difficult rep-resentation theoretic questions. In this talk, we explain one aspect ofthis connection and describe the progress which has been made onthe representation theoretic questions. In particular, we describe
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the classification of the maximal closed positive-dimensional sub-groups of the simple linear algebraic groups, and indicate the inher-ent difficulties encountered in attempting to establish the analogousclassification for the finite quasisimple groups of Lie type. Finally,we discuss the application of the classification to some recent workon the lattice of subgroups of the classical simple algebraic groups.
Ecole Polytechnique Federale de Lausanne
Invariant random subgroups of locally finite groups
Simon Thomas
Let G be a countable discrete group and let SubG be the compactspace of subgroups H 6 G. Then a probability measure ν on SubGwhich is invariant under the conjugation action of G on SubG iscalled an invariant random subgroup. In this talk, I will discuss theinvariant random subgroups of inductive limits of finite alternatinggroups.
Rutgers University
The bouquet algebra of toric ideals
Apostolos Thoma
To any toric ideal, encoded by an integer matrix A, we associatea matroid structure called the bouquet graph of A, and introduceanother toric ideal called the bouquet ideal of A, which captures theessential combinatorics of the initial toric ideal. The new bouquetframework allows us to answer some open questions about toric ide-als. For example, we provide a characterization of toric ideals forwhich the following sets are equal: the Graver basis, the univer-sal Groebner basis, any reduced Groebner basis and any minimalgenerating set. Moreover, we show that toric ideals of hypergraphsencode all toric ideals.
Ioannina University
13
Twenty years of attacks on unipotent elements
Sukru Yalcınkaya
Black box groups were introduced as an idealised setting forrandomised algorithms for solving permutation and matrix groupproblems in computational group theory. A black box group is ablack box (or an oracle, or a device, or an algorithm) operating withbinary strings of uniform length which encrypt (not necessarily in aunique way) elements of some finite group. Group operations, takinginverses and deciding whether two strings represent the same groupelements are done by the black box. In this context, a natural task isto find a probabilistic algorithm which determines the isomorphismtype of a group within given arbitrarily small probability of error.More desirable algorithms, constructive recognition algorithms, arethe ones producing an isomorphism between a black box copy of afinite group and its natural copy.
The presentation of the groups of Lie type is based on the socalled unipotent elements (elements whose orders are the charac-teristic of the underlying field). Therefore, the construction of aunipotent element in groups of Lie type is the fundamental partof the constructive recognition algorithms in black box group the-ory. Over twenty years, there has not been an efficient algorithmconstructing a unipotent element in black box groups of Lie type.
In this talk, I will reduce the problem of constructing a unipotentelement in a black box group of Lie type of odd characteristic tothe groups PGL2. Then, by using the geometry of involutions inPGL2, I will talk about the construction of the underlying blackbox projective plane and black box field. This procedure readilygives an efficient (in time polynomial in the input length) algorithmwhich constructs a unipotent element in black box groups of Lietype of odd characteristic. I will also explain how our algorithmworks for the groups PGL2 in characteristic 2.
This is a joint work with Alexandre Borovik.
Istanbul Universitesi
14
On Rogers-Ramanujan functions, binary quadraticforms and eta-quotients
Hamza Yesilyurt
In a handwritten manuscript published with his lost notebook,Ramanujan stated without proofs forty identities for the Rogers-Ramanujan functions. We give a brief history of the Rogers-Ra-manujan functions and Ramanujan’s identities for them. We thenobserve that the form that appears in Ramanujan’s identities canbe obtained from a Hecke action on a certain family of eta prod-ucts. We establish further Hecke-type relations for these functionsinvolving binary quadratic forms. These observations enable us tofind new identities for the Rogers–Ramanujan functions and alsoto use such identities in return to find identities involving binaryquadratic forms.
Bilkent Universitesi
Part II
Contributed Talks
15
17
A survey of noncommutative multiplicative ideal theory
Evrim Akalan
The aim of this talk is to survey noncommutative rings from theview point of multiplicative ideal theory. The main classes of ringsconsidered are maximal orders, Krull orders (rings), unique fac-torization rings, generalized Dedekind prime rings and hereditaryNoetherian prime rings. We report on the description of reflexiveideals in Ore extensions and Rees rings. Further we give necessaryand sufficient conditions for well-known classes of rings to be max-imal orders, and we propose a polynomial type’s generalization ofhereditary Noetherian prime rings.
This is a joint work with H. Marubayashi.
Hacettepe Universitesi
Smooth values of Piatetski Shapiro sequences
Yıldırım Akbal
A number is said to be y-smooth if all of its prime divisors areat most y. The disribution of smooth integers has been heavilyinvestigated since such numbers appear in many places throughoutanalytic and computational number theory (see e.g. [1], [2]). In thistalk, we give several distribution results for smooth values of ⌊nc⌋,where ⌊x⌋ = max{n ∈ N : n ≤ x}, n runs through positive integersand c > 1 is fixed.
References[1] A. Hildebrand, G. Tenenbaum. On integers free of large prime factors.Trans. Amer. Math. Soc., 296, no. 1, pp 265-290. 1986
[2] A. Granville. Smooth numbers: computational number theory and beyond.
Algorithmic Number Theory: lattices, number fields, curves and cryptography,
267-323, Math. Sci. Res. Inst. Publ., 44, Cambridge Univ. Press, Cambridge,
2008.
Bilkent Universitesi
18
Derivations and generalized derivations in prime ringsatisfying some conditions on multilinear polynomials
Emine Albas
Let R be an associative prime ring of characteristic differentfrom 2. Throughout this talk, unless specially stated, Z(R) alwaysdenotes the center of R, U the Utumi quotient ring of R and Cextended centroid of R (i.e., C = Z(U)). An additive mappingF : R → R is called a generalized derivation if there exists a deriva-tion d : R → R such that F (xy) = F (x)y + xd(y) holds for allx, y ∈ R. The generalized derivation covers both the concepts ofderivation and left multiplier mapping. The left multiplier mappingmeans an additive mapping F : R → R such that F (xy) = F (x)yholds for all x, y ∈ R.
In this talk, we aim to prove the following:
Main Theorem. Let R be a noncommutative prime ring ofcharacteristic different from 2 with Utumi quotient ring U and ex-tended centroid C, and f(x1, . . . , xn) be a multilinear polynomialover C, which is not central valued on R. Suppose that F and Gare two generalized derivations of R and d is a nonzero derivationof R such that
d(F (f(r))f(r)− f(r)G(f(r))) = 0
for all r = (r1, . . . , rn) ∈ Rn, then one of the following holds:1. there exist a, p, q ∈ U and λ ∈ C such that F (x) = ax +
xp + λx and G(x) = px + xq for all x ∈ R, with [c, a − q] = 0 andf(x1, . . . , xn)
2 is central valued on R;2. there exists a ∈ U such that F (x) = xa and G(x) = ax for
all x ∈ R;3. there exist a, b ∈ U and λ ∈ C such that F (x) = λx+xa− bx
and G(x) = ax+xb for all x ∈ R, with b+αc ∈ C for some α ∈ C;4. R satisfies s4 and there exist a, b ∈ U and λ ∈ C such that
F (x) = λx+ xa− bx and G(x) = ax+ xb for all x ∈ R;5. there exist a′, b ∈ U and δ a derivation of R such that F (x) =
a′x+xb−δ(x) and G(x) = bx+δ(x) for all x ∈ R, with [c, a′] = 0 andf(x1, . . . , xn)
2 is central valued on R. Our work is mainly motivatedby the works in [4] and [6].
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This is joint work with B. Dhara and N. Argac.
References[1] N. Argac and V. De Filippis, Actions of generalized derivations on multilinearpolynomials in prime rings, Algebra Colloq. 18 (Spec 01) (2011), 955-964.[2] J. Bergen, I. N. Herstein, J. W. Kerr, Lie ideals and derivations of primerings, J. Algebra 71 (1981), 259-267.[3] C. L. Chuang, GPI’s having coefficients in Utumi quotient rings, Proc. Amer.Math. Soc. 103 (3) (1988), 723-728.[4] V. De Filippis, O.M. Di Vincenzo, Vanishing derivations and centralizersof generalized derivations on multilinear polynomials, Comm. Algebra, 40 (6)(2012), 1918-1932.[5] V. De Filippis, A product of two generalized derivations on polynomials inprime rings, Collect. Math., 61 (3) (2010), 303-322.[6] V. De Filippis, Cocentralizing and vanishing derivations on multilinear poly-nomials in prime rings, Siberian Mathematical Journal, 50 (4) (2009), 637-646.[7] T. L. Wong, Derivations with power central values on multilinear polynomi-als, Algebra Colloquium 3 (4) (1996), 369-378.
Ege Universitesi
On the classical Krull-Remak-Schmidt theorem
Mustafa Kemal Berktas
Recall (e.g. from [4]) that the Krull-Remak-Schmidt holds inthe additive category A provided
1. every object is a biproduct of indecomposable object, and
2. if M1 ⊕ . . . ⊕ Mm∼= N1 ⊕ . . . ⊕ Nn with each Mi and each
Nj an indecomposable object in A, then n = m and, afterrenumbering Mi
∼= Ni for each i.
This statement can be viewed as a version of the FundamentalTheorem of Arithmetic. In this talk, we will give historical back-ground information and some recent results on the classical Krull-Remak-Schmidt Theorem in the context of groups, modules andsome categories. For instance, the first such uniqueness theoremwas stated by Wedderburn in the context of finite groups.
References[1] Berktas M. K., A uniqueness theorem in a finitely accessible additive cate-gory. Algebr. Represent. Theor. 17, 1009–1012 (2014).
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[2] Facchini, A., Direct sum decompositions of modules with semilocal endo-morphism rings. Bull. Math. Sci. 2, 225–279 (2012).[3] Krause, H., Uniqueness of uniform decompositions in abelian categories. J.Pure Appl. Algebra 183, 125–128 (2003).
[4] Leuschke, G. J. and Wiegand, R., Cohen-Macualay representations. Amer.
Math. Soc., 2012.
Usak Universitesi
Envelopes in Mc− groups
Tuba Cakmak
In [1], Altınel and Baginski showed that a nilpotent subgroupof an Mc−group is contained in a definable nilpotent subgroup ofthe same nilpotency class. Here definable is in the sense of firstorder mathematical logic and in the language of groups. A groupis said to be Mc if it has minimal condition on centralizers. Intheir proof, Altınel-Baginski have introduced some subgroups (En)as tools. In this talk we will prove some properties of these groupsindependently from the Mc condition and improve some results ofAltınel-Baginski. If time remains we will discuss approaches to thestabilization problem and give some examples.
This is a part of my thesis work supervised by Tuna Altınel andErdal Karaduman.
References[1] T. Altınel, P. Baginski, definable envelopes of nilpotent subgroups of groupswith chain conditions on centralizers, Proceedings of the American Mathemat-ical Society, 2014, 142 (5), 1497-1506.
[2] R. M. Bryant, Groups with the minimal condition on centralizers, Journal
of Algebra, 1979, 60, 371-383.
Ataturk Universitesi
New 2-edge-balanced graphs from bipartite graphs
Cafer Calıskan
Let G be a graph of order n satisfying that there exists λ ∈ Z+
for which every graph of order n and size t is contained in exactly λ
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distinct subgraphs of the complete graph Kn isomorphic to G. ThenG is called t-edge-balanced and λ the index of G. In this article, newexamples of 2-edge-balanced graphs are constructed from bipartitegraphs and some further methods are introduced to obtain morefrom old.
Kadir Has Universitesi
Local Langlands correspondence
Yusuf Danısman
Langlands correspondence establishes a connection between Ga-lois representations and representations of automorphic forms. Itembodies Langlands’ vision of a non-abelian class field theory forlocal and global cases.
One of the aims of Local Langlands conjecture is to show theequivalence of the local factors of the Galois and automorphic sides[4]. This is important to show the uniqueness of the correspondence.Let k be a nonarchemedian local field. In [1], [2] and [3] somelocal factors of automorphic side for the symplectic similitude groupGSp4(k) are computed. By using the construction of Piatetski-Shapiro in [5] we show the existence of the local factors for theirreducible representations of GSp 4(k).
References[1] Danisman Y. Regular poles for the p-adic group GSp 4(k). Turk. J. Math.2014; 38: 587-613.[2] Danisman Y. Regular poles for the p-adic group GSp 4(k)-II. Turk. J. Math.;Doi: 10.3906/mat-1404-72.[3] Danisman Y. Local factors of nongeneric supercuspidal representations ofGSp4. Mathematische Annalen 2015; 361: 1073-1121.[4] Gan W. T., Takeda S. The local Langlands conjecture for GSp 4(k). Ann.Math. 2011, 173: 1841-1882.
[5] Piatetski-Shapiro I. L-functions for GSp 4(k). Pacific J Math Olga Taussky
Todd Memorial Issue 1997; 259–275.
Mevlana Universitesi
22
Classification of some solvable Leibniz algebras
Ismail Demir
Leibniz algebras are non-antisymmetric generalization of Lie al-gebras. Classification of all solvable Lie algebras is presently un-solved and is very difficult problem. Due to lack of antisymmetryin Leibniz algebras, the problem of classifying all solvable Leibnizalgebras is more complicated. We give classification of solvable Leib-niz algebras with one dimensional derived subalgebra. We use thecanonical forms for the congruence classes of matrices of bilinearforms to obtain our result.
References[1] Demir, I., Misra, K.C, Stitzinger, E. On some structures of Leibniz alge-bras, in Recent Advances in Representation Theory, Quantum Groups, Alge-braic Geometry, and Related Topics, Contemporary Mathematics, vol. 623,Amer. Math. Soc., Providence, RI, 2014, pp. 41-54.
[2] Teran, F.D. Canonical forms for congruence of matrices: a tribute to H. W.
Turnbull and A. C. Aitken. 2nd meeting on Linear Algebra, Matrix Analysis
and Applications(ALAMA 2010), Valencia(Spain), 2010.
North Carolina State University
Generalized skew derivations in prime rings
M. Pınar Eroglu
Let R be a ring with center Z(R). By a derivation of R, we meanan additive map D from R into itself satisfying the rule D(xy) =D(x)y + xD(y) for all x, y ∈ R. An additive map G : R → R iscalled a generalized derivation of R if there exists a derivation D ofR such that G(xy) = G(x)y + xD(y) for all x, y ∈ R.
Let σ be an automorphism of R. An additive map D : R → R iscalled a σ-derivation (or a skew derivation) on R ifD(xy) = D(x)y+σ(x)D(y) for all x, y ∈ R. An additive mapping F : R → R is calleda generalized σ-derivation (or a generalized skew derivation) on R ifthere exists an additive mappingD on R such that F (xy) = F (x)y+σ(x)D(y) for all x, y ∈ R. The map D is uniquely determined by Fand it is called an associated additive map of F . Moreover, it turnsout that D is always an σ-derivation. The generalized σ-derivationgeneralize both σ-derivation and generalized derivations.
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A well known result proved by Posner [1], states that if d is aderivation of a prime ring R such that the commutators [d(x), x] ∈Z(R) for all x ∈ R, then either d = 0 or R is commutative. Then theresult of Posner was extended by many authors to a more generalizedsituation considering power values of generalized (skew) derivationson Lie ideals in prime rings
(see for example, [2, 3]
). Our aim here
is to extend a similar situation in [3] to power central values of thegeneralized skew derivation on Lie ideals in prime rings.
This is a joint work with Nurcan Argac.
References[1] Posner EC. (1957). Derivations in prime rings, Proc. Amer. Math. Soc. 8:1093-1100.[2] De Filippis V. (2006) Generalized derivations and commutators with nilpo-tent values on Lie ideals.
[3] Carini L., De Filippis V., Scudo G. (2014) Power-commuting generalized
Skew derivations in prime rings.
Dokuz Eylul Universitesi
Some classes of automorphisms of free metabeliannilpotent Lie algebras
Sehmus Fındık
Let L be the finitely generated free metabelian nilpotent Lie al-gebra over a field of characteristic 0. We describe the groups of inner,outer,normal,normally outerandouter normal automorphisms of L.
Some of the results are jointly obtained with Vesselin Drensky.2010 Mathematics Subject Classification: 17B01, 17B30, 17B40.Key words: Free metabelian nilpotent Lie algebras, inner-outer-
normal automorphisms, Baker-Campbell-Hausdorff Formula.
References[1] S. Fındık (2010) Normal and normally outer automorphisms of free metabeliannilpotent Lie algebras, Serdica Mathematical Journal, 36, 171-210.
[2]V. Drensky, S. Fındık (2012) Inner and outer automorphisms of free metabelian
nilpotent Lie algebras, Communications in Algebra, 40, 4389-4403.
Cukurova Universitesi
24
Bilinear recurrence sequences
Betul Gezer
Linear reccurence sequences have been playing an important rolein number theory. But there are also sequences which satisfy abilinear recurrence relation.
A bilinear recurrence sequence is a sequence (hn) which satisfiesthe recurrence relation
hnhn−k =∑
i+j=k;1≤i≤j
τihn−jhn−k+j (1)
where τ1, τ2, ..., τ⌊k/2⌋ are constants.If P = (0, 0) and Q = (x, y) are non-singular points on an elliptic
curve E over Q then bilinear recurrence sequence with k = 4 ariseseither from
hn = (−1)n(n+1)/2xn−1x2n−2...x
n−11 xn
0
where (xn, yn) = Q+nP or an elliptic divisibility sequence [1]. Therecurrences describing these sequences involve divisions by anotherterm. It is clear that, these sequences turn out to have rationalterms. The question of when a bilinear sequence have only integerterms has received much attention in the literature [2, 3, 4]. Inthis talk we are interested in integrality properties of the sequenceswhich can be expressed in terms of the x-coordinates of the points(xn, yn) = Q+ nP .
This is joint work with Osman Bizim.
References[1] G. Everest, A. van der Poorten, I. Shparlinski, T. Ward, Recurrence Se-quences, Mathematical Surveys and Monographs 104, AMS, Providence, RI,2003.[2] S. Fomin, A. Zelevinsky, The Laurent phenomen, Adv. Appl. Math. 28(2002) 119-144.[3] D. Gale, The strange and suprising saga of the Somos sequences, Math.Intelligencer 13 (1) (1991) 40-42.
[4] D. Gale, Somos sequence update, Math. Intelligencer 13 (4) (1991) 49-50.
Uludag Universitesi
25
A recognition algorithm for twisted modules
Kubra Gul
Let X be a set of n × n matrices with entries in F = Fq andG = ⟨X⟩ be isomorphic to H acting irreducibly on W that is atwisted module of dimension n(d2 < n < d3) of high weights
λ1, λ2, λd−2, λd−1, 2λ1, 2λd−1.
In this paper, we present a Las Vegas algorithm that constructs arepresentation of G of dimension d.
This is a joint work with Nurullah Ankaralıoglu.
References[1] Corr BP. Estimation and computation with matrices over finite fields. Phd,The University of Western Australia Department of Mathematics, Australia,2014.[2] Glasby SP, Leedham-Green CR, O’Brien EA. Writing projective represen-tations over subfields. Journal of Algebra 2006; 295: 51-61.[3] Lubeck F. Small degree representations of finite Chevalley groups in definingcharacteristic. London Mathematical Society 2003; 4: 135-169.
[4] Magaard K, O’Brien EA, Seress A. Recognition of small dimensional rep-
resentations of general lineer groups. J. Avustralian Math. Soc. 2008; 85:
229-250.
Ataturk Universitesi
Waring’s problem with Piatetski-Shapiro numbers
Ahmet Muhtar Guloglu
We investigate in various ways the representation of a large nat-ural number as a sum of a fixed power of Piatetski-Shapiro numbers,thereby establishing a variant of the Hilbert-Waring problem withnumbers from a sparse sequence.
This is a joint work with Yıldırım Akbal.
Bilkent Universitesi
26
Maximal non-Noetherian subrings
Noomen Jarboui
Let R be a subring of a Noetherian ring S. R is said to bea maximal non-Noetherian subring of S if R is non-Noetherian andany subring of S that properly containsR is Noetherian. In this talk,we first present some characterizations of such domains in severalcases. If the ring R is semi-local, (R,S) is a residually algebraic pairand R is a maximal non- Noetherian subring of S, we give sharpupper bounds for the number of rings and the length of chains ofrings in [R,S], the set of intermediary rings. The second part ofthis talk is concerned with the prime spectrum of maximal non-Noetherian subrings of a given domain. It is proved that if R isa maximal non-Noetherian subring of S, then R is a stably strongS-domain and that R is universally catenarian iff S is universallycatenarian. Our main results lead to new examples of stably strongS-domains and universally catenarian domains.
References[1] A. Ayache, M. Ben Nasr and N. Jarboui, PID pairs of rings and maximalnon-PID subrings. Math. Z. 268 (2011), no. 3-4, 635-647.[2] A. Ayache and N. Jarboui, Maximal non-Noetherian subrings of a domain.J. Algebra 248 (2002), no. 2, 806-823.[3] N. Jarboui and A. Jerbi, A note on maximal non-Noetherian subrings of adomain. Beitr. Algebra Geom. 53 (2012), no. 1, 159-172.
[4] S. Visweswaran, Intermediate rings between D+I and K[y1, · · · , yt]. Comm.
Algebra 18 (1990), no. 2, 309-345.
University of Sfax
The dual Steenrod algebra andthe overlapping shuffle product
Shizuo Kajı
The mod 2 Steenrod algebra A2 appears in topology as an algebraover F2 consisting of the stable cohomology operations on the mod2 cohomology group of a space (a classical reference is [3]). It hasmany applications such as in Adam’s solution of the Hopf invariantone problem and the computation of the stable homotopy groups.
27
Algebraically, A2 is defined to be a quotient of so-called themod 2 Leibniz–Hopf algebra F2 (cf. [1]), which is the free associa-tive algebra over F2 generated by countably many indeterminantsS1, S2, S3, . . . of degSi = i. This algebra is equipped with a co-commutative co-product given by
∆(Sn) =n∑
i=0
Si ⊗ Sn−i (S0 := 1),
which makes it a graded Hopf algebra. Then, A2 is defined to bethe quotient Hopf algebra of F2 by the ideal generated by the Ademrelations:
SiSj −⌊i/2⌋∑k=0
(j − k − 1
i− 2k
)Si+j−kSk.
Denote the quotient map by π : F2 → A2. The image of the gener-ator π(Si) is usually denoted by Sqi.
The structure of A2 has been extensively studied and, in par-ticular, Milnor [2] proved that the linear dual A∗2 is a polynomialalgebra. By taking the dual of π, we can regard A∗2 as a sub Hopf-algebra of F∗2 , which also has an interesting combinatorial property:The product in F∗2 is given by the overlapping shuffle product. Thisis described in terms of the combinatorics of words on integers,though we do not give the slightly involved definition in this ab-stract. By investigating the overlapping shuffle product, we recoversome of the classical results on the structure of A∗2 (mainly due toMilnor [2]) purely combinatorially.
This is a joint work with Neset Deniz Turgay.
References[1] M. Hazewinkel, The algebra of quasi-symmetric functions is free over theintegers, Adv. Math. 164, 283–300 (2001).[2] J. Milnor, The Steenrod algebra and its dual, Ann. Math. 67, 150–171(1958).
[3] N.E. Steenrod and D.B.A. Epstein, Cohomology Operations. Princeton:
Princeton Univ. Press, (1962).
Yamaguchi University
28
On bipolar soft rough sets
Faruk Karaaslan
Concept of rough set was introduced by Pawlak [3] as an alter-native approach to fuzzy set defined Zadeh [4]. Soft set theory wasproposed by Molodtsov [2] as a mathematical tool for dealing withuncertainty. Soft sets were combined with rough sets by Feng etal. [1]. In this study, we define notion of bipolar soft rough set andbipolar soft rough set operations such as union, intersection andcomplement. We also investigate some properties of bipolar softrough set operations.
References[1] F. Feng, X. Liu, V. Leoreanu-Fotea, and Y. B. Jun, Soft sets and soft roughsets, Information Sciences, 181(6), 1125-1137, 2011.[2] D. Molodtsov, Soft set theory first results, Computers and Mathematics withApplications, 37, 19-31, 1999.[3] Z. Pawlak, Rough sets, International Journal of Computer and InformationSciences, 11(5), 341-356, 1982.[4] L. A. Zadeh, Fuzzy Sets, Inform. and Control, 8, 338-353, 1965.
Cankırı Karatekin Universitesi
On circulant-type matrices with generalizednumber sequences
Emrullah Kırklar
Recently, there are huge amount of papers on circulant-type ma-trices and their properties. Some of them give useful theorems forcirculant-type matrices with well-known number sequences. Thisstudy provides some identities for circulant-type matrices with gen-eralized number sequences of second order.
This is a joint work with Fatih Yılmaz.
References[1] S.-Q. Shen, J.-M. Cen, Y. Hao, On the determinants and inverses of circulantmatrices with Fibonacci and Lucas numbers, Appl. Math. Comput. 217 (2011),no.23, 9790-9797.[2] N. Shen, Z. Jiang, J. Li, On explicit determinants of the RFMLR andRLMFL circulant matrices involving certain famous numbers, Wseas Trans-actions on Mathematics, 2013:42-53.
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[3] T. Xu, Z. Jiang, Explicit Determinants of the RFPrLrR Circulant andRLPrFrL Circulant matrices Involving Some Famous Numbers, Abstract andApplied Analysis, 2014, Article ID 647030, 9 p.
[4] A. F. Horadam, Basic Properties of a Certain Generalized Sequence of Num-
bers, The Fibonacci Quarterly 3.3 (1965): 161-176.
Gazi [email protected]
Some model theory of finite group scheme actions
Piotr Kowalski
I will recall how one can understand an iterative Hasse-Schmidtderivation as an infinite sequence of actions of finite group schemescoming from the additive group. Then I will describe how to gen-eralize the results of Martin Ziegler about model theory of iterativeHasse-Schmidt derivations to the case of actions of arbitrary finitegroup schemes and formal groups.
This is a joint work with my PhD student Daniel Hoffmann.
Uniwersytet [email protected]
Andrews and Bressoud style partition identities
Kagan Kursungoz
We propose a method to construct a variety of partition iden-tities at once. The main applications are all-moduli generalizationof some of Andrews’ results in [Andrews, Parity in partition iden-tities. Ramanujan Journal 23:45-90 (2010)] and Bressoud’s evenmoduli generalization of Rogers-Ramanujan-Gordon identities, andtheir counterparts for overpartitions due to Lovejoy et al. and Chenet al. We obtain unusual companion identities to known theoremsas well as to the new ones in the process. The novelty is that themethod constructs solutions to functional equations which are sat-isfied by the generating functions. In contrast, the conventionalapproach is to show that a variant of well-known series satisfies thesystem of functional equations, thus reconciling two separate linesof computations.
Sabancı [email protected]
30
The group of units in integral group ring Z[T × C2]
Omer Kusmus
Constructing the group of units in the integral group ring ofa given group is still a classical open problem. It is known for thegroup G×C2 while G = S3, D8, P and Cn. In this study, we considerthe problem for the dicyclic group of order 12 as follows
T =< a, b : a6 = 1, b2 = a3, bab3 = a5 >
and show that U(Z[T ×C2]) ∼= (F33 o F5)o (T ×C2) where Fi is afree group of rank i.
References[1] P. J. Allen and C. Hobby, A Characterization of Z[A4], J. Algebra, 66,(1980), 534-543;[2] P. J. Allen and C. Hobby, A Characterization of Z[S4], Commun. Algebra,16, (1988), 1479-1505;[3] G. Higman, Units in Group Rings, Proc. London Math. Soc., 46, (1940),231-248.[4] E. Jespers, Free Normal Complements and the Unit Group of Integral GroupRings, Proc. Amer. Math. Soc., 122, (1994), 59-66.[5] E. Jespers and M. M. Parmenter, Units of Group Rings of Groups of Order16, Glasgow Math. J., 35, (1993), 367-379.[6] G. Karpilovsky, Commutative Group Algebras, Marcel Dekker, New York,1983.[7] Y. Li, Units of Z(G× C2), Quaestiones Mathematicae, 21, (1998), 201-218.[8] R. M. Low, Units in Integral Group Rings for Direct Products, PhD Thesis,Western Michigan University, Kalamazoo, MI, (1998).[9] M. M. Parmenter, Torsion-free Normal Complements in Unit Groups ofIntegral Group Rings, C. R. Math. Rep. Acad. Sci Canada, 12, (1990), 113-118.[10]M.M. Parmenter, Free Torsion-free Normal Complements in Integral GroupRings, Commun. Algebra, 21, (1993), 3611-3617.[11] R. M. Low, On the Units of the Integral Group Ring Z[G×Cp], J. AlgebraAppl., 7, (2008), 393-403.[12] C. P. Milies, S. K. Sehgal, An Introduction to Group Rings, Kluwer Aca-demic Publishers, New York, 2002.
[13] S. K. Sehgal, Units in Integral Group Rings, Longman Scientific & Tech-
nical, Essex, 1993.
Yuzuncu Yıl Universitesi
31
Uniformly resolvable cycle decomposition with four cycles
Ugur Odabası
A decomposition of a graph G is a set H = {H1, H2, ..., Hk} ofedge-disjoint subgraphs of G such that
k∪i=1
E(Hi) = E(G).
A H-decomposition is a decomposition of G such that Hi∼= H for
all Hi ∈ H. If each Hi is a cycle (or union of cycles), then H iscalled a cycle decomposition. A parallel class or resolution class ofthe decompositionH of G is a subset of vertex-disjoint graphs whoseunion is the vertex set of G. A decomposition is called resolvable if ithas a partition of the subgraphs Hi into parallel classes. A parallelclass is called uniform if for all 1 ≤ i ≤ k and a H ∈ H, Hi
∼= H. Inthis case the parallel classes are called H-factors and we say G has aH-factorization. A {F k1
1 , F k22 , . . . , F kl
l }−factorization of a graph Gis a resolvable decomposition which consists precisely of ki parallelclasses isomorphic to Fi−factors.
The case H ∼= K2 is known as 1-factorization. Another impor-tant case is 2-factorization where every vertex in the graph H hasdegree 2. Whether there exists a 2−factorization of Kv (or for evenv, 2−factorization of Kv − I where I is a 1−factor) with prescribed2−factors is a long standing important problem in combinatorialdesign theory.
In this talk, we focus mainly on an {Cr14 , Cr2
m , Cr32m, Cr4
4m}−fac-torization of Kv − I.
This is a joint work with Sibel Ozkan and supported by The Sci-entific and Technological Research Council of Turkey (TUBITAK)under project number 113F033.
Istanbul Universitesi
32
On semigroup presentations that define a group
Belgin Ozer
We consider the finite semigroup presentations of the form
P = ⟨ a1, . . . , an | w1 = a1, . . . , wn = an ⟩
and their Adian graphs. It is known that if both Adian graphs of Pare connected and if one of the Adian graphs of P is a cycle graphthen P defines a group (see [1]). We extend this result to certainpresentations such that neither of the Adian graphs are cycle graphs.
2000 Mathematics Subject Classification: 20M05This is a joint work with Gonca Ayık.
References[1] G. Ayık, H. Ayık, Y. Unlu, On Semigroup Presentations and Adian Graphs,Discrete Math., 308 no. 11 (2008), 2288–2291.[2] H. Ayık, C.M. Campbell, J.J. O’Connor, N. Ruskuc, The semigroup effi-ciency of groups and monoids, Math. Proc. Roy. Irish Acad., 100A (2) (2000),171—176.[3] H. Ayık, F. Kuyucu, B. Vatansever, On Semigroup Presentations and Effi-ciency, Semigroup Forum, 63 (2002), 231–242.[4] C. M. Campbell, J. D. Mitchell, N. Ruskuc, On Defining Groups Efficientlywithout Using Inverses, Math. Proc. Cambridge Philos. Soc., 133 (2002),31–36.[5] P. M. Higgins, Techniques of Semigroup Theory, Oxford University Press,1992.
Gaziantep Universitesi
Orbits and test elements in free Leibnizalgebras of rank two
Zeynep Ozkurt
Let F be the free Leibniz algebra of rank two over a field Kof characteristic 0 freely generated by x1 and x2. It is shown thatan endomorphism of F which preserves the orbit of a nontrivialelement is an automorphism. Using this result we determine sometest elements of F .
33
References[1] Abdykhalikov, A. T.; Mikhalev, A. A.; Umirbaev, U.U. Automorphism ofTwo-Generated Free Leibniz Algebras. Commun. Algebra 2001, 29(7), 2953-2960.[2] Drensky, V.; Yu, J. T. Orbits in Free Algebras of Rank Two. Commun.Algebra 1998, 26(6), 1895-1906.[3] Ivanov, S. V. On Endomorphisms of Free Groups that Preserve Primitivity.Arch. Math.(Basel) 1999, 72(2), 92-100.[4] Loday, J.-L.; Prashvili, T. Universal Enveloping Algebras of Leibniz algebrasand (co)Homology. Math. Ann. 1993, 296, 139-158.[5] Mikhalev, A. A.;Umirbaev, U. U. Subalgebras of Free Leibniz Algebras.Commun. Algebra 1998, 26, 435-446.[6] Mikhalev, A. A; Zolotykh, A. A. Automorphisms and primitive Elements ofFree Lie Superalgebras.Commun. Algebra 1994, 22(14), 5889-5901.[7] Mikhalev, A. A; Yu, J. T. Primitive, almost primitive, test and primitiveelements of free algebras with the Nielsen-Schreier property, J. Algebra 2003,228, 603-623.[8] Nielsen, J. Die Isomorphismen der allgemeinen unendlishen Gruppe mit zweiErzeugenden, Math. Ann. 1918, 78, 269 272.[9] Shpilrain, V. Recognizing Automorphisms of the Free Groups. Arch. Math.1994, 62, 385-392[10] Shpilrain, V. Generalized primitive elements of a free group. Arch. Math(Basel)1998, 71(4), 270-278[11] Turner, E. Test words for automorphisms of free groups, Bull. LondonMath. Soc. 1966, 28 , 255-263.[12] Van Den Essen, A.; Shpilrain, V. Some Combinatorial Questions aboutPolynomial Mappings. J. Pure. Appl. Algebra 1997, 119(1), 47-52.
Cukurova Universitesi
The Beta G-star relation on the set ofsubmodules of any module
Nurhan Sokmez
In this work, we say submodulesX and Y ofM are β∗g equivalent,Xβ∗gY , if and only if Y + K = M for every K E M such thatX +K = M and X + T = M for every T E M such that Y + T =M . It is proved that the β∗g relation is an equivalent relation andhas good behaviour with respect to addition of submodules andhomomorphisms.
34
Results
Lemma 1. The β∗g relation is an equivalence relation.
Lemma 2. Let X,Y ≤ M . The following statements are equivalent.(i) Xβ∗gY .(ii) For every T E M such that X + Y + T = M , X + T = M andY + T = M .
Proposition 3. Let X, Y ≤ M . If Xβ∗gY , then X+YX ≪ g
MX and
X+YY ≪ g
MY .
Theorem 4. Let X, Y ≤ M such that X ≤ Y +A and Y ≤ X+B,where A, B ≪ g M . Then Xβ∗gY .
Lemma 5. Let X ≤ M . X ≪ g M if and only if Xβ∗g0.
Corollary 6. Let X,Y ≤M and Xβ∗gY . If X≪g M , then Y ≪g M .
Lemma 7. Let X1, X2, Y1, Y2 ≤ M such that X1β∗gY1 and X2β
∗gY2.
Then (X1 +X2)β∗g (Y1 + Y2).
Corollary 8. Let X1, X2, . . . , Xn, Y1, Y2, . . . , Yn ≤ M and Xiβ∗gYi
for every i = 1, 2, ..., n. Then X1+X2+ ...+Xnβ∗gY1+Y2+ ...+Yn.
Corollary 9. Let X1, X2, . . . , Xn, Y ≤ M and Xiβ∗gY for every
i = 1, 2, . . . , n. Then X1 +X2 + · · ·+Xnβ∗gY .
Lemma 10. Let f : M −→ N be an R−module homomorphismand X,Y ≤ M . If Xβ∗gY , then f (X)β∗gf (Y ).
Corollary 11. Let X, Y, Z ≤ M . If Xβ∗gY, thenX+ZZ β∗g
Y+ZZ .
Proposition 12. Let X, Y ≤ M . If Xβ∗gY and Y is an essentialmaximal submodule of M , then X ≤ Y .
Definition 13. Let M be an R−module and U, V ≤ M . If U+V =M and U ∩V ≪ g M , then V is called a weak g-supplement of U inM . If every submodule of M has a weak g-supplement in M , thenM is called a weakly g-supplemented module.
Proposition 14. Let Xβ∗gY in M .(i) If X has an essential g-supplement V in M , then V is also ag-supplement Y in M .(ii) If X has an essential weak g-supplement V in M , then V is alsoa weak g-supplement Y in M .
35
This is joint work with Celil Nebiyev.
References[1] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, 1974.[2] G. F. Birkenmeier, F. T. Mutlu, C. Nebiyev, N. Sokmez and A. Tercan,Goldie*-supplemented Modules, Glasgow Mathematical Journal, 52A, 41-52(2010).[3] F. Kasch, Modules and Rings, London New York, 1982.[4] B. Kosar, C. Nebiyev and N. Sokmez, G-Supplemented Modules, UkrainianMathematical Journal (Accepted).[5] J. Clark, C. Lomp, N. Vanaja, R. Wisbauer, Lifting Modules Supplementsand Projectivity In Module Theory, Frontiers in Mathematics, Birkhauser, Basel,2006.[6] N. Sokmez, B. Kosar, C. Nebiyev, Genellestirilmis Kucuk Alt Moduller,XXIII. Ulusal Matematik Sempozyumu, Erciyes Universitesi, Kayseri, (2010).[7] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach,Philadelphia, 1991.
Ondokuz Mayıs Universitesi
Indispensable free resolutions
Mesut Sahin
We will talk about monomial curves with small embedding di-mensions whose minimal free resolutions are indispensable.
The results which will be presented are joint work with V. Barucci(Rome University) and R. Froberg (Stockholm University), see [1].
References[1] V. Barucci, R. Froberg, M. Sahin, On free resolutions of some semigrouprings, J. Pure Appl. Algebra, 218 (6) (2014), 1107-1116.
Hacettepe Universitesi
Some ancient puzzles and Alcuin’s sequence
Murat Sahin
We present some ancient puzzles. One of those problems is theflask-sharing problem. Alcuin’s sequence which is defined as thenumber of incongruent integer triangles of perimeter n turn out tobe useful in this problem. Also, it’s solutions are related to the
36
number of partitions of n into exactly 3 parts. Then, we introducea new family of sequences {tk(n)}∞n=−∞ for given positive integerk. We call these new sequences as generalized Alcuin’s sequencesbecause we get Alcuin’s sequence when k = 3. Also, {tk(n)}∞n=0
counts the number of some partitions of n − k. We investigateinteresting properties of generalized Alcuin’s sequences.
References[1] D. Panario, M. Sahin and Q. Wang, Generalized Alcuins Sequence, TheElectronic Journal of Combinatorics, Volume 19, Issue 4, Paper P55, 2012;[2] D. J. Bindner and M. Erickson, Alcuin’s Sequence, Amer. Math. Monthly119, 115-121, 2012;
[3] D. Olivastro. Ancient Puzzles, Bantam Books, New York, NY, 1993.
Ankara Universitesi
Bi-periodic Lucas sequences
Elif Tan
In this study, we consider the bi-periodic Lucas sequences {pn},defined by for n ≥ 2
pn =
{bpn−1 + pn−2, if n is evenapn−1 + pn−2, if n is odd
with initial values p0 = 2 and p1 = a, where a, b are nonzero num-bers. We introduce the bi-periodic incomplete Lucas sequences thatgives the incomplete Lucas sequence as a special case. Let n be apositive integer and l be an integer such that
0 ≤ l ≤⌊n2
⌋.
The bi-periodic incomplete Lucas numbers are defined as
pn (l) = aξ(n)l∑
i=0
n
n− i
(n− i
i
)(ab)⌊
n2 ⌋−i .
We also give recurrence relations and the generating function ofthese sequences. Also, we give a relation between bi-periodic in-complete Fibonacci sequences and bi-periodic incomplete Lucas se-quences.
37
References[1] M. Edson and O. Yayenie. A new generalizations of Fibonacci sequencesand extended Binet’s Formula, Integers 9, (A48) (2009), 639-654.;[2] Ramırez, Bi-periodic incomplete Fibonacci sequence, Ann. Math. Inform.42 (2013), 83–92.;[3] E. Tan and A. B. Ekin, Bi-periodic incomplete Lucas sequence, Ars Combi-natoria (accepted).;
[2] O. Yayenie, A note on generalized Fibonacci sequeence, Appl. Math. Com-
put. 217 (2011) 5603-5611.
Ankara Universitesi
Outer automorphisms of free groups
Vladimir Tolstykh
Let Fn be a free group of finite rank n. A result by Khramtsov[4]stating that the outer automorphism group Out(Fn) of Fn is comp-lete provided that n>3 was a natural development of earlier resultsby Dyer and Formanek on description of the automorphism groupsof finitely generated relatively free groups. In particular, Dyer andFormanek proved that the automorphism group Aut(Fn) is completeprovided that n> 2 [3]. Later, Bridson and Vogtmann [1] obtainednew proofs of the results by Dyer and Formanek and by Khramtsovtreating both groups Aut(Fn) and Out(Fn) in a uniform way.
For every infinitely generated free group F, the automorphismgroup Aut(F ) of F is also complete [5], and a natural candidatefor a tool which could allow one to treat both groups Aut(F ) andOut(F ) in a uniform way might be the small index property for rel-atively free algebras. An infinitely generated relatively free algebraF is said to have the small index property if any subgroup Σ of thegroup Γ = Aut(F) of index at most rank(F) contains the pointwisestabilizer Γ(U) of a subset U of F of cardinality less than rank(F).For instance, the small index property is true for all infinitely gen-erated free nilpotent groups [6]; as far as absolutely free groups areconcerned the small index property has been established only forgroups of countably infinite rank [2].
Theorem 1. Let F be a free group of countably infinite rank.Then the outer automorphism group Out(F ) of F is complete.
38
The proof is based upon a group-theoretic characterization ofa suitable class of involutions in the group Out(F ) followed by agroup-theoretic characterization of the images under the naturalhomomorphism Aut(F ) → Out(F ) of the stabilizers of primitiveelements in the group F, which uses the small index property for F.
References[1] M. Bridson, K. Vogtmann, Automorphisms of automorphism groups of freegroups, J. Algebra, 229 (2000) 785–792.[2] R. M. Bryant, V. A. Roman’kov, The automorphism groups of relativelyfree algebras, J. Algebra 209 (1998) 713–723.[3] J. Dyer, E. Formanek, The automorphism group of a free group is complete,J. London Math. Soc. 11 (1975) 181–190.[4] D. G. Khramtsov, Completeness of groups of outer automorphisms of freegroups, in Group-theoretic investigations (Russian), Akad. Nauk SSSR Ural.Otdel., Sverdlovsk (1990) 128–143.[5] V. Tolstykh, The automorphism tower of a free group, J. London Math. Soc.(2) 61 (2000) 423–440.
[6] V. Tolstykh, The small index property for free nilpotent groups, Comm.
Alg. 43 (2015) 447–459.
Istanbul Arel Universitesi
Grobner-Shirshov basis for affine Weyl group of type Cn
Ugur Ustaoglu
Grobner-Shirshov bases and reduced form of the elements werealready found for the Coxeter groups of type An, Bn and Dn in [1].They also proposed a conjecture for the general form of Grobner-Shirshov bases for all Coxeter groups. In [2], an example was givento show that the conjecture is not true in general. The Grobner-Shirshov bases of the other finite Coxeter groups are given in [3]and [4]. This paper is another example of finding Grobner-Shirshovbases for groups, defined by generators and defining relations. In[5], we calculated Grobner-Shirshov Basis and reduceds words forAn. In this talk, we deal with the affine Weyl group of type Cn,denoted by Cn, which is an infinite Coxeter group. Using definingrelations, we able to find the reduced Grobner-Shirshov basis of Cn
and classify all reduced words of the affine Weyl group Cn.This is a joint work with Erol Yılmaz.
39
References[1] L. A. Bokut and L. S. Shiao, Grobner-Shirshov bases for Coxeter groups,Comm. Algebra 29 (2001), 4305-4319.[2] Y. Chen and C. Liu, Grobner-Shirshov Bases for Coxeter groups I,arXiv:0910.0096v1, (2009).[3] D. Lee, Grobner-Shirshov Bases and Normal Forms for the Coxeter GroupsE6 and E7, Advances in Algebra and Combinatorics, World Scientific, pp. 243-255, (2008).[4] O. Svechkarenko, Grobner-Shirshov Bases for the Coxeter Group E8, MasterThesis, Novosibirsk State University, (2007).[5] E. Yılmaz, C. Ozel and U. Ustaoglu, Grobner-Shirshov basis and reducedwords for the affine Weyl group An, Journal of Algebra and Its Applications,13 (6), (2014).
Abant Izzet Baysal [email protected]
The Siegel-Weil formula and its applications
Cetin Urtis
In this talk we give a review of the Siegel-Weil formulas and itsregularized versions for dual pairs. Then we give some applicationsof the Siegel-Weil formula such as special values of L−functions, ba-sis problem for hermitian orthogonal groups and poles of Eisensteinseries and L−functions.
TOBB Ekonomi ve Teknoloji Universitesi
Jordan groups and Model Theory
David Bradley-Williams
We survey some of the interactions between the study of Jordangroups, a certain class of permutation groups, and the structurespreserved by the action of such groups.
University of Central Lancashire
40
On the cohomological dimension of localcohomology modules
Tugba Yıldırım
Let R be a Noetherian ring, I an ideal of R and M an R-module.Then the i-th local cohomology module of M with support in I isdefined as Hi
I(M) = lim→
Ext iR(R/In,M), and one of the important
invariant related to local cohomology modules is the cohomologicaldimension of M with respect to I, denoted by cd(I,M), and definedas: cd(I,M) = sup {i ∈ N | H i
I (M) = 0}.In a joint work with Vahap Erdogdu, for an R-module M with
cd(I,M) = c, we show the existence of a descending chain of idealsI = Ic ) Ic−1 ) · · · ) I0 of R such that for each 0 ≤ i ≤ c − 1,cd(Ii,M) = i and that the top local cohomology module Hi
Ii(M)
is not Artinian. We then give sufficient conditions for an arbitrarynon-negative integer t to be a lower bound for the cohomologicaldimension of a finitely generated R-module M , and use this to con-clude that in non-catenary Noetherian local integral domains, thereexist prime ideals that are not set theoretic complete intersection.
References
[1] M. P. Brodmann and R. Y. Sharp, Local Cohomology, 2nd ed., CambridgeStudies in Advanced Mathematics, Vol. 136, Cambridge University Press, Cam-bridge, 2013. An algebraic introduction with geometric applications;
[2] V. Erdogdu and T. Yıldırım, On The Cohomological Dimension of Local
Cohomology Modules, arXiv:1504.01148, 2015(submitted).
Istanbul Teknik Universitesi
Properties of the induced operators on the space ofhomogeneous polynomials
Yousef Zamani
Induced operators over tensor powers are studied extensively[4], [5]. In this article we will study the algebraic and geometricproperties of induced operators over the vector space of homoge-neous polynomials. In other words, we will assume that V is the
41
complex vector space of homogeneous linear polynomials in the vari-ables x1, . . . , xm and for any T ∈ L (V ) we will define the inducedoperator
P (T ) : Hd[x1, . . . , xm] → Hd[x1, . . . , xm]
byP (T )q(x1, . . . , xm) = q(Tx1, . . . , Txm).
Here L (V ) is the space of linear operators on V and Hd[x1, . . . , xm]is the complex vector space of homogeneous polynomials of degreed in the variables x1, . . . , xm. We obtain many algebraic propertiesof the operator P (T ) as well as some geometric properties. In theforthcoming work, the same study will be done for the restriction ofP (T ) on the symmetry class of polynomials [1, 6, 7].
At the present stage no knowledge of the theory of relative sym-metric polynomials is required.
This a joint work with Mahin Ranjbari [8].
References[1] E. Babaei, Y. Zamani and M. Shahryari, Symmetry classes of polynomials,to appear in Comm. Algebra.[2] R. Bhatia, Positive Definite Matrices, Princeton University Press, 2007.[3] R. Bhatia and J. A. Dias da Silva, Vartition of induced linear operators,Linear Algebra Appl. 341 (2002) 391- 402.[4] M. Marcus, Finite Dimensional Multilinear Algebra, Part I, Marcel Dekker,Inc., New York, 1973.[5] R. Merris, Multilinear Algebra, Gordon and Breach Science Publisher, Am-sterdam, 1997.[6] M. Shahryari, Relative symmetric polynomials, Linear Algebra Appl. 433(7)(2010) 1410–1421.[7] Y. Zamani and E. Babaei, The dimensions of cyclic symmetry classes ofpolynomials, J. Algebra Appl. 13(2) (2014) Article ID 1350085 (10 pages).
[8] Y. Zamani and M. Ranjbari, Induced operators on the space of homogeneous
polynomials, submitted.
Sahand University of [email protected]
Part III
Posters
43
45
Generalized ⊕− Supplemented Lattices
Cigdem Bicer
Let L be a complete modular lattice. L is said to have (D3)property if a∧b is a direct summand of L for every direct summandsa, b of L with 1 = a ∨ b. L is called a generalized ⊕−supplementedlattice if every element of L has a generalized supplement that isa direct summand of L. Let L be a generalized ⊕−supplementedlattice, u ∈ L and u = (u ∧ a)∨(u ∧ b) for every a, b ∈ L with 1 = a⊕b, then 1/u is also generalized⊕−supplemented. If a∧r(L) = r (a/0)for every direct summand a of a generalized ⊕−supplemented latticeL with (D3) property , then for every direct summand u of L, u/0is generalized ⊕−supplemented.
This is joint work with Celil Nebiyev.
References[1] R. Alizade and E. Toksoy, Cofinitely Weak Supplemented Lattices, IndianJ. Pure Appl. Math., 40 No.5, 1 – 9 (2009).[2] R. Alizade and E. Toksoy, Cofinitely Supplemented Modular Lattices, Ara-bian Journal for Science and Engineering, 36 No. 6, 919-923 (2011).[3] C. Bicer, Radikal Tumlenmis Kafesler, Yuksek Lisans Tezi, Ondokuz MayısUniversitesi, Fen Bilimleri Enstitusu, Samsun, 2011.[4]G. Calugareanu, 2000, Lattice Concepts of Module Theory, Kluwer AcademicPublisher, Dordrecht, Boston, London, 2000.[5] H. Calısıcı and E. Turkmen, Generalized ⊕−Supplemented Modules, Alge-bra and Discrete Mathematics, 10 No.2, 10-18 (2010).
[6] N. Sokmez, B. Kosar, C. Nebiyev, Genellestirilmis Kucuk Alt Moduller,
XXIII. Ulusal Matematik Sempozyumu, Erciyes Universitesi, Kayseri, (2010).
Ondokuz Mayıs Universitesi
cigdem [email protected]
Some comments on soft expert sets
Hilal Donmez
Soft set theory was introduced by Molodtsov [3] in 1999. Untilnow its many versions have been developed and applied a lot of areafrom algebra to decision making problems. One of these versions issoft expert set which is introduced by Alkhazaleh and Salleh [1] in2011 and allow to know the opinion of more than one expert inone model. In this paper, for further study on the soft expert sets,
46
we have made fit this concept which is important for developmentof the concept of the soft sets by decontaminating from its owninconsistencies. We then propose and apply an algorithm for thenew concept by using the new definitions and Maji et al’s algorithmwithout reduction in [2]. We finally discuss this concept later onworks.
This is a joint work with Serdar Enginoglu.
References[1] Alkhazaleh S., Salleh A. R., Soft expert set, Hindawi Publishing CorporationAdvances in Decision Sciences, vol. 2011, Article ID 757868, 12 pages, 2011.[2] Maji P. K., Roy A. R., Biswas R., An application of soft sets in a decisionmaking problem, Computers & Mathematics with Applications, vol. 44, no.8-9, pp. 1077-1083, 2002.
[3] Molodtsov D., Soft set theory-first results, Computers & Mathematics with
Applications, vol. 37, no.4-5, pp.19-31, 1999.
Ondokuz Mart Universitesi
Grafiklerin cebirsel islemlerinde tutarlılık
Serdar Enginoglu
Verilen bir fonksiyonla bu fonksiyona ait grafigin birbirini tekturlu olarak belirledigi uygun sartlarda, fonksiyon yerine kume uze-rinde calısma 20. yuzyılın ikinci yarısında Zadeh tarafından or-taya atılan bulanık (fuzzy) kumelerle [4] hız kazandı. Pawlak’ınyaklasımlı (rough) kumeleri [3], Molodtsov’un esnek (soft) kumeleri[2] vb. diger tur kumelerin belirsizligi modemellemede ulastıklarıbasarıların etkisiyle elestirel tutumdan uzak kalınmıs ve herseyinyolunda oldugu gibi bir iyimserlik havasına girilmistir. Deyim yerin-de ise yasa tanımazlık denebilecek bu gidis Alkhazaleh ve Salleh’in[1] esnek uzman (soft expert) kumeleri vb. ile devam etmektedir.Bu calısmada, bu tur kumelerin cebirsel islemlerinde meydana ge-len tutarsızlık sorunu ele alındı ve bu sorunun cozumu icin gereklitemellendirme calısmaları uzerinde duruldu.
Bu calısma Hilal Donmez ile ortak bir calısmadır.
References[1] Alkhazaleh S., Salleh A.R., Soft expert set, Hindawi Publishing CorporationAdvances in Decision Sciences, vol. 2011, Article ID 757868, 12 pages, 2011.[2] Molodtsov D., Soft set theory-first results, Computers & Mathematics withApplications, vol. 37, no.4-5, pp.19-31, 1999.
47
[3] Pawlak, Z., Rough sets, Int. J. of Information and Computer Sciences, 11(5),341-356, 1982.
[4] Zadeh, L., Fuzzy sets, Information and Control, 8, 338-353, 1965.
Onsekiz Mart Universitesi
Primary decomposition of cellular binomial ideals
Zekiye Eser
The goal of this abstract is to summarize the results in [1], con-cerning the primary decomposition of binomial ideals, and especiallyof cellular binomial ideals. The fact that any binomial ideal has aneffectively computable decomposition as a finite intersection of cel-lular binomial ideals provides both theoretical and computationalmotivation for this study.
Binomial ideals, and in particular, their primary decompositions,have various applications. Over an algebraically closed field, theradical, associated primes, and primary components of a binomialideal are also binomial, see [2]. These results, due to Eisenbud andSturmfels [2] are computationally effective results, but not combi-natorially explicit.
The search for more effective results lead us to study the specialclass of cellular binomial ideals. Without any restrictions on thebase field, we compute the hull and provide an unmixed decomposi-tion of a cellular binomial ideal. The latter had already been provedby Eisenbud and Sturmfels in characteristic zero, and conjecturedto also hold in positive characteristic. Over an algebraically closedfield, we also compute the minimal primary components of such anideal; this is then combined with our other results to yield a clean,explicit cellular binomial primary decomposition.
Let k be a field; throughout this article, k denotes an algebraicclosure of k. A binomial in k[x] = k[x1, . . . , xn] is a polynomialthat has at most two terms. A binomial ideal is an ideal generatedby binomials. An ideal I ⊆ k[x] is cellular if every variable xi
is either a nonzerodivisor modulo I or is nilpotent modulo I. Thenonzerodivisor variables modulo a cellular binomial ideal I are calledthe cellular variables of I. If I is a cellular binomial ideal, and∆ ⊆ {1, . . . , n} indexes the cellular variables of I, then I is called∆-cellular.
48
If ∆ ⊆ {1, . . . , n}, we denote N∆ = {u ∈ Nn | ui = 0 for i /∈ ∆},and define Z∆ analogously. We also use ∆c to denote the comple-ment {1, . . . , n}r∆.
A partial character on Zn is a group homomorphism ρ : Lρ → k∗,
where Lρ is a subgroup of Zn and k∗ is the multiplicative group ofthe field k. Given a partial character (Lρ, ρ) on Zn, we define thecorresponding lattice ideal via
I(ρ) ..= ⟨xu − ρ(u− v)xv | u− v ∈ Lρ⟩ ⊆ k[x].
If (Lρ, ρ) is a partial character on Zn, then the lattice ideal I(ρ)is {1, . . . , n}-cellular. Moreover if I is a ∆-cellular binomial ideal ink[x], there exists a partial character (Lρ, ρ) on Z∆ such that
I ∩ k[N∆] = I(ρ).
If k is algebraically closed, the primary decomposition of I(ρ)can be explicitly determined in terms of extensions of Lρ to itssaturation Sat(Lρ) ..= (Q ⊗Z Lρ) ∩ Zn. A partial character (Lρ, ρ)is saturated if Sat(Lρ) is equal to Lρ.
Eisenbud and Sturmfels [2, Theorem 2.1.c] proved that a bino-mial ideal P ⊆ k[x] is prime if and only if there exists a subset∆ ⊂ {1, . . . , n} and a saturated partial character (Lχ, χ) on Z∆,such that
P = k[x] · I(χ) + ⟨xi | i ∈ ∆c⟩.
Let I be a ∆-cellular binomial ideal in k[x]. A lattice L ⊆ Z∆ isassociated to I if there exists a witness monomial m ∈ k[N∆c
] suchthat (I : m) ∩ k[N∆] = I(ρ) for some partial character ρ : L → k
∗
on Z∆.
Definition 15. Let I be a ∆-cellular binomial ideal in k[x], and let(Lρ, ρ) be the partial character on Z∆ that satisfies I∩k[N∆] = I(ρ).A lattice L associated to I is said to be embedded if it properlycontains Lρ and Sat(Lρ) = Sat(L). We define
Memb(I) ..= ⟨witness monomials of embedded associated lattices to I⟩.
Lemma 16. ([1, Lemma4.1]). Let I be a ∆-cellular binomial idealin k[x]. Let (Lρ, ρ) be a partial character on Z∆ such that I ∩k[N∆] = I(ρ). The minimal associated primes of I are of the form
49
k[x] · P + ⟨xi | i ∈ ∆c⟩, where P ⊂ k[N∆] is a minimal associatedprime of I(ρ). If k is algebraically closed, the minimal associatedprimes of I are
k[x] · I(χj) + ⟨xi | i ∈ ∆c⟩ for j = 1, . . . , g,
where g and χ1, . . . , χg are given by Corollary 2.5 in [2] applied tothe lattice ideal I(ρ).
We compute the minimal primary components of a cellular bino-mial ideal. This information is then used to give an explicit formulafor the hull of such an ideal (the intersection of the minimal pri-mary components) and an unmixed decomposition, both of whichhold without any assumptions on the base field.
Theorem 17. ([1, Theorem 5.1 and Theorem 5.3]) Let I be a ∆-cellular binomial ideal in k[x], where k is algebraically closed andchar(k) = p ≥ 0. Let (Lρ, ρ) be the partial character on Z∆ suchthat I ∩ k[N∆] = I(ρ). Consider g, ρ1, . . . , ρg and χ1, . . . , χg as inCorollary 2.5 in [2], so that I(ρℓ) is the I(χℓ)-primary component ofI(ρ) for ℓ = 1, . . . , g. By Lemma 2, the minimal associated primesof I are
Pℓ = I(χℓ) + ⟨xi | i ∈ ∆c⟩ for ℓ = 1, . . . , g.
For ℓ = 1, . . . , g, the Pℓ-primary component of I is((I + I(ρℓ)) : (
∏i∈∆
xi)∞)+Memb(I). (2)
Eisenbud and Sturmfels in [2] express the primary componentsof a binomial ideal as hulls of cellular binomial ideals. We give morecombinatorial information about the hull operation.
Theorem 18. ([1, Theorem 2.10]) Let I be a ∆-cellular binomialideal in k[x]. Denote by Hull(I) the intersection of the minimalprimary components of I. Then Hull(I) = I + Memb(I). Assumenow that k is algebraically closed. If (Lρ, ρ) is a partial characteron Z∆ such that I ∩ k[N∆] = I(ρ), and g and ρ1, . . . , ρg are as inCorollary 2.5 in [2], so that I(ρ) = ∩g
ℓ=1I(ρℓ) is a minimal primarydecomposition, then
50
Hull(I) = I+Memb(I) =
g∩ℓ=1
[((I+I(ρℓ)) : (
∏i∈∆
xi)∞)+Memb(I)
]
is a minimal primary decomposition of Hull(I).
If we combine our computation of the hull of a cellular binomialideal with [2, Theorem 7.1’], we slightly improve the main result in[2].
If q is a positive integer and b = t1−t2 is a binomial, where t1, t2are terms, set b[q] = tq1− tq2. For I a binomial ideal, we define its qthquasipower to be the ideal I [q] = ⟨b[q] | b ∈ I is a binomial⟩.
Corollary 19. ([1, Corollary 3.2]). Let I be a binomial ideal ink[x], where k is algebraically closed. If P is an associated prime ofI, write ∆(P ) for the set of nonzerodivisor variables of P .1. If char(k) = p > 0, and q = pe is sufficiently large, a minimalprimary decomposition of I into binomial ideals is given by
I =∩
P∈Ass(k[x]/I)
[((I+P [q]) : (
∏i∈∆(P )
xi)∞)+Memb
((I+P [q]) : (
∏i∈∆(P )
xi)∞)]
.
2. If char(k) = 0, a minimal primary decomposition of I into bino-mial ideals is given by
I =∩
P∈Ass(k[x]/I)
[((I + (P ∩ k[N∆(P )])
): (∏
i∈∆(P ) xi)∞)+
Memb
((I + (P ∩ k[N∆(P )])
): (∏
i∈∆(P ) xi)∞)]
.�
References[1] Zekiye Sahin Eser and Laura Felicia Matusevich, Cellular binomial ideals,arXiv:math.AC/1409.0179v1
[2] David Eisenbud and Bernd Sturmfels, Binomial ideals, Duke Math. J., 84
(1996), No.1, 1-45.
Zirve Universitesi
51
Some results on ring of rhotrices
Tugce Guler, Ummahan Acar, Emre Ciftlikli
Our aim in this paper is to study the ring of rhotrices 5-dimension.We show that ring R of rhotrices 5-dimension is a star ring also weprove that ring of rhotrices is isomorphic to opposite ring of it.
References[1] The concept of Rhotrix in Mathematical Enrichment, International Journalof Mathematical Education in Science and Technology, Vol. 34, No. 2, 2003 pp.175-179.[2] Rhotrix Vector Spaces, Department of Mathematical Education in Scienceand Technology, Vol. 41, No. 4, 15 june 2010, 531-573.[3] A remark on the classificationsof rhotrices as abstract structures Interna-tional Journal of Physical Sciences Vol. 4 (9), pp. 496-499, September, 2009
[4] A New Expression for Rhotrix Advanced in linear algebra Matrix Theory,
2014, 4, 128-133.
Mugla Sıtkı Kocman Universitesi
[email protected], [email protected],
The structure of the second derived ideal of freecentre-by-metabelian Lie rings
Nil Mansuroglu
We study the free centre-by-metabelian Lie ring which is thefree Lie ring satisfying the property that the second derived idealis contained in the centre. We find explicit generating sets for thehomogeneous and fine homogeneous components of the second de-rived ideal. Each of these components is a direct sum of a freeabelian group and a (possibly trivial) elementary abelian 2-group.Our generating sets are such that some of their elements generatethe torsion subgroup while the remaining ones freely generate a freeabelian group. A key ingredient of our approach is the determina-tion of the dimensions of the corresponding homogeneous and finehomogeneous components of the free centre-by-metabelian Lie alge-bra over fields of characteristic other than 2. For that we exploit asix-term exact sequence of modules over a polynomial ring that isoriginally defined over the integers, but turns into a sequence whose
52
terms are projective modules after tensoring with a suitable field.Our results correct a partly erroneous theorem in the literature.
This is joint work with Ralph Stohr.
Ahi Evran Universitesi
Magic cross of Boca Raton
Lohans de Oliveira Miranda, Liuhan Oliveira de Miranda,Lossian Barbosa Bacelar Miranda
We have established a linear operator in R2n, n = 2, which allowsus to build a large class of pairs of diagonals of square matricesof order n, with positive integer elements, and such that the sumof the elements of each one of the diagonals is equal to the magic
constant n+n3
2 . The operator also provides explicit solutions to someproblems concerning to the sum of subsets. The weakness of thepresented method is not able to generate all the pairs of diagonals.
Federal University of Piaui, Federal Institute of Education Sci-ence and Technology of Piaui
[email protected], [email protected]
G-radical supplemented modules
Celil Nebiyev
In this work, g-radical supplemented modules are defined andsome properties of these modules are investigated. It is proved thatthe finite sum of g-radical supplemented modules is g-radical sup-plemented. It is also proved that every factor module and everyhomomorphic image of a g-radical supplemented module is g-radicalsupplemented. Let R be a ring. Then RR is g-radical supplementedif and only if every finitely generated R-module is g-radical supple-mented.
Key words: Small Submodules, Radical, Supplemented Mod-ules, Radical (Generalized) Supplemented Modules.
53
Results
Definition 1. Let M be an R-module and U, V ≤ M . If M = U+Vand U ∩ V ≤ RadgV , then V is called a generalized radical supple-ment (briefly, g-radical supplement) of U in M . If every submoduleof M has a generalized radical supplement in M , then M is calleda generalized radical supplemented (briefly, g-radical supplemented)module.
Clearly we see that every g-supplemented module is g-radicalsupplemented.
Lemma 2. Let M be an R-module and U, V ≤ M . Then V is ag-radical supplement of U in M if and only if M = U + V andRm ≪g V for every m ∈ U ∩ V .
Lemma 3. Let M be an R-module, M1, U,X ≤ M and Y ≤ M1.If X is a g-radical supplement of M1 + U in M and Y is a g-radical supplement of (U +X)∩M1 in M1, then X+Y is a g-radicalsupplement of U in M .
Lemma 4. Let M = M1 + M2. If M1 and M2 are g-radical sup-plemented, then M is also g-radical supplemented.
Corollary 5. Let M = M1 + M2 + ... + Mk. If Mi is g-radicalsupplemented for every i = 1, 2, ..., k, then M is also g-radical sup-plemented.
Lemma 6. Let M be an R−module, U, V ≤ M and K ≤ U . If V isa g-radical supplement of U in M , then (V +K) /K is a g-radicalsupplement of U/K in M/K.
Lemma 7. Every factor module of a g-radical supplemented moduleis g-radical supplemented.
Corollary 8. The homomorphic image of a g-radical supplementedmodule is g-radical supplemented.
Lemma 9. Let M be a g-radical supplemented module. Then everyM−generated module is g-radical supplemented.
Corollary 10. Let R be a ring. Then RR is g-radical supplementedif and only if every finitely generated R−module is g-radical supple-mented.
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Lemma 11. Let V be a g-radical supplement of U in M. If U isa generalized maximal submodule of M , then U ∩ V is a uniquegeneralized maximal submodule of V .
References[1] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, 1974.[2] F. Kasch, Modules and Rings, London New York, 1982.[3] B. Kosar, C. Nebiyev and N. Sokmez, G-Supplemented Modules, UkrainianMathematical Journal (Accepted).[4] J. Clark, C. Lomp, N. Vanaja, R. Wisbauer, Lifting Modules Supplementsand Projectivity In Module Theory, Frontiers in Mathematics, Birkhauser, Basel,2006.[5] N. Sokmez, B. Kosar, C. Nebiyev, Genellestirilmis Kucuk Alt Moduller,XXIII. Ulusal Matematik Sempozyumu, Erciyes Universitesi, Kayseri, (2010).[6] W. Xue, Characterizations of Semiperfect and Perfect Rings, PublicationsMatematiques, 40, 115-125 (1996).[7] Y. Wang and N. Ding, Generalized Supplemented Modules, Taiwanese Jour-nal of Mathematics, 10 No.6, 1589-1601 (2006).[8] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach,Philadelphia, 1991.
[9] H. Zoschinger, Komplementierte Moduln uber Dedekindringen, Journal of
Algebra, (29):42–56 (1974).
Ondokuz Mayıs Universitesi
On a new family of k-Fibonacci and k-Lucas numbers
Engin Ozkan, Ipek Altun, Ali Aykut Gocer
We prove some theorems concerning a new family of Fibonaccinumbers defined in [10]. We give some relationship between thefamily and Fibonacci and Lucas number. Then we give a new familyof k -Lucas numbers and establish some properties of the relation tothe Lucas numbers and the family of Lucas numbers.
55
References[1] Akbulak, M. and Bozkurt, D., On the order-m generalized Fibonacci k-numbers, Chaos Soliton Fract. (2009), doi:10.1016/j.chaos.2009.03.019.[2] Campbell, C. M. and Campbell, P. P., The Fibonacci length of certaincentro-polyhedral groups, J. Appl. Math. Comput. 19, No. 1-2, (2005), 231-240.[3] Deveci, O., Karaduman, E. and Campbell, C. M., On the k-Nacci Sequencesin Finite Binary Polyhedral Groups, Algebra Colloquium(AC), 18, Special Issue,(2011) 945-954.[4] Grabowski, A. and Wojtecki, P., Lucas numbers and generalized Fibonaccinumbers, Form. Math. 12 (2004) 329-334.[5] Gyoung-Sik, C., Hwang, Suk-Geun; Kim, Ik-Pyo and Shader, Bryan L., (±1)Invariant sequences and truncated Fibonacci Sequences, Linear Algebra and itsApplications 395, (2005), 303-312.[6] Hartwig, R. E., Note on a linear difference equation, Am. Math. Monthly113, (3), (2006) 250–256.[7] Karaduman, E and Deveci,O. K-nacci Sequences in Finite Triangle Groups.Discrete Dynamics in Nature and Society, (2009), 453750-1-453750-10.[8] Kilic, E. and Tasci, D., Generalized order-k Fibonacci and Lucas numbers,Rocky Mountain J. Math. 38 (2008) 1991–2008.[9] Koshy, T., Fibonacci and Lucas Numbers with Applications, A Wiley-Interscience Publication, John Wiley & Sons Inc.,2001, ISBN: 978-0-471-39969-8[10] Mikkawy, M. and Sogabe, T., A new family of k-Fibonacci numbers, Ap-plied Mathematics and Computation 215 (2010) 4456–4461.[11] Ocal, A.A. , Tuglu, N. and Altinisik, E., On the representation of k-generalized Fibonacci and Lucas numbers, Appl. Math. Comput. 170 (2005).[12] Ozgur N. Y., Generalizations of Fibonacci and Lucas Sequences. Note diMatematica, 21, (2002), 113-125[13] Ozkan, E. On Truncated Fibonacci Sequences, Indian J. Pure of and App.Mathematics, 38(4), (2007), 241-251.[14] Ozkan, E., Aydın, H. and Dikici, R. 3-step Fibonacci series modulo m.Applied Mathematics and Computation,143, (2003),165-172.[15] Stanimirovic, P. S. , Nikolov, J. and Stanimirovic, I., A generalization ofFibonacci and Lucas matrices, Discrete Appl. Math. 156 (2008) 2606–2619.[16] Taher, R. B. And Rachidi, M., On the matrix power and exponential by ther-generalized Fibonacci sequences methods: the companion matrix case, LinearAlgebra Appl. 370 (2003) 341–353.
[17] Tasci, D. and Kilic, E., On the order-k generalized Lucas numbers, Appl.
Math. Comput. 155 (2004) 637–641.
Erzincan Universitesi
[email protected], [email protected],
aykut [email protected]
56
On LA-semigroup with its soft ideals
Aslıhan Sezgin Sezer
In this study, soft intersection LA-semigroups, soft intersectionleft (right, two-sided) ideals, (generalized) bi-ideals, interior ide-als, quasi-ideals in LA-semigroups are defined, their examples andproperties are given and their interrelations are obtained. Moreover,regular and intra-regular LA-semigroups are characterized via thesesoft intersection ideals and it is shown that all these ideals coincidein an intra-regular LA-semigroup with left identity.
References[1] N. Cagman and S. Enginoglu, Soft set theory and uni-int decision making,Eur. J. Oper. Res. 207 (2010), 848-855.[2] M. A. Kazim, M. Naseeruddin, On almost semigroups, The Alig. Bull.Math. 2 (1972), 1-7.[3] D. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999),19-31.[4] A. Sezgin and A. O. Atagun, On operations of soft sets, Comput. Math.Appl. 61 (5) (2011), 1457-1467.
[5] A. Sezgin Sezer, Soft union rings, ideals and bi-ideals; a new approach to
ring theory I, Knowledge-Based Systems, 36 (2012) 300-314
Amasya Universitesi
f-orthomorphisms over the second order dual of f-algebra
Sebnem Yıldız
Let A be an Archimedean f -algebra with unit and L, M betwo f -modules over A. In this paper assume that T is an f -orthomorphisms from L to M over A. We investigate some specialproperties of the second adjoint T” of T over A”.
Ahi Evran Universitesi
57
Complex factorization of some two-periodic linearrecurrence systems by eigenvalues method
Semih Yılmaz
Let a0, a1, b0, b1 are real numbers. The two-periodic secondorder linear recurrence system {vn} is defined by v0 := 0, v1 ∈ Rand for n ≥ 1
v2n : = a0v2n−1 + b0v2n−2
v2n+1 : = a1v2n + b1v2n−1.
It is difficult to calculate the n − th term of the sequence {vn}.We present a method to facilitate this diffıculty by using eigenval-ues. Also, we find the factorizations of this recurrence systems.Hence, we get the factorizations of some sequences: Pell, Jacobstal,Mersenne etc. which are special cases of {vn} .References[1] Yılmaz, S. Ekin, A. B. Complex factorization of some two-periodic linearrecurrence systems. Commun. Fac.Sci.Univ. Ank. Series A1, Vol 63, No 2,129-134.[2] Daniel Panario, Murat Sahin, Qiang Wang; A family of Fibonacci-like con-ditional sequences, INTEGERS Electronic Journal of Combinatorial NumberTheory, 13, A78, 2013.[3] Heleman R. P. Ferguson; The Fibonacci Pseudogroup, Characteristic Poly-nomials and Eigenvalues of Tridiagonal Matrices, Periodic Linear RecurrenceSystems and Application to Quantum Mechanics, The Fibonacci Quarterly,16.4 (1978): 435–447.[4] Curtis Cooper, Richard Parry; Factorizations Of Some Periodic Linear Re-currence Systems, The Eleventh International Conference on Fibonacci Num-bers and Their Applications, Germany (July 2004).[5] Nathan D. Cahill, John R. D’Errico, John P. Spence; Complex Factorizationsof the Fibonacci and Lucas Numbers, The Fibonacci Quarterly, 41, No.1 (2003),13-19.
[6] www.oeis.org , The On-Line Encyclopedia of Integer Sequences.
Kırıkkale Universitesi
Part IV
Participants andCommittees
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61
Participants of Antalya Algebra Days XVII
1. Adnan Cihan Cakar (Bilkent Universitesi)
2. Ahmet Muhtar Guloglu (Bilkent Universitesi)
3. Alev Altınel (Sakarya Universitesi)
4. Alexandre Borovik (University of Manchester)
5. Ali Nesin (Istanbul Bilgi Universitesi)
6. Alper Kutlu (Canakkale Onsekiz Mart Universitesi)
7. Alper Ulker (Ege Universitesi)
8. Anargyros Katsampekis (Mimar Sinan Guzel Sanatlar Universitesi)
9. Apostolos Thoma (University of Ioannina)
10. Aslıhan Sezgin Sezer (Amasya Universitesi)
11. Ayse Ayran (Canakkale Onsekiz Mart Universitesi)
12. Ayse Berkman (Mimar Sinan Guzel Sanatlar Universitesi)
13. Ayse Mutlu (Canakkale Onsekiz Mart Universitesi)
14. Aysenur Altan (Istanbul Universitesi)
15. Belgin Ozer (Gaziantep Universitesi)
16. Betul Gezer (Uludag Universitesi)
17. Burak Kaya (Rutgers University)
18. Burcu Cınarcı (Istanbul Universitesi)
19. Burcin Saltık (Ege Universitesi)
20. Busra Buyraz (Bilkent Universitesi)
21. Cafer Calıskan (Kadir Has Universitesi)
22. Cansu Aktepe (Orta Dogu Teknik Universitesi)
23. Cansu Yılmazer (Ege Universitesi)
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24. Celil Nebiyev (Ondokuz Mayıs Universitesi )
25. Cemile Kurkoglu (Bilkent Universitesi)
26. Cennet Eskal (Osmaniye Korkut Ata Universitesi)
27. Cetin Urtis (TOBB Ekonomi ve TeknolojiUniversitesi)
28. Cisil Karaguzel (Bilkent Universitesi)
29. Cigdem Bicer (Ondokuz Mayıs Universitesi )
30. David Bradley Williams (University of Central Lancashire)
31. David Pierce (Mimar Sinan Guzel Sanatlar Universitesi)
32. Dilek Ersalan (Cukurova Universitesi)
33. Donna Testerman (Ecole Polytechnique)
34. Ebru Yigit (Cukurova Universitesi)
35. Egemen Dirik (Orta Dogu Teknik Universitesi)
36. Ehud Hrushovski (Hebrew University)
37. Ekin Ozman (Bogazici Universitesi)
38. Elif Tan (Ankara Universitesi)
39. Emine Albas (Ege Universitesi)
40. Emre Ciftlikli (Mugla Sıtkı Kocman Universitesi)
41. Emrullah Kırklar (Gazi Universitesi)
42. Engin Ozkan (Erzincan Universitesi)
43. Erdal Karaduman (Ataturk Universitesi)
44. Erdal Ozyurt (Adnan Menderes Universitesi)
45. Eren Sen (Ege Universitesi)
46. Evrim Akalan (Hacettepe Universitesi)
47. Faruk Karaaslan (Cankırı Karatekin Universitesi)
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48. Fatih Yılmaz (Gazi Universitesi)
49. Feza Arslan (Mimar Sinan Guzel Sanatlar Universitesi)
50. Fikri Kaplan (Bilkent Universitesi)
51. Giovanni Falcone (Universita di Palermo)
52. Gonca Kızılaslan (Kırıkkale Universitesi)
53. Gokcen Buyukbas Cakar (Bilkent Universitesi)
54. Gokhan Benli (Orta Dogu Teknik Universitesi)
55. Hamza Yesilyurt (Bilkent Universitesi)
56. Hasan Huseyin Top (Dokuz Eylul Universitesi)
57. Hatice Mutlu (Bilkent Universitesi)
58. Hilal Donmez (Canakkale Onsekiz Mart Universitesi)
59. Inna Capdeboscq (The University of Warwick)
60. Ipek Altun (MEB)
61. Ipek Tuvay (Gebze Teknik Univeristesi)
62. Ismail Demir (North Carolina State University)
63. Jarboui Noomen (Faculty Of Sciences Of Sfax)
64. Kagan Kursungoz (Sabancı Universitesi)
65. Kenan Sapan (Canakkale Onsekiz Mart Universitesi)
66. Kıvanc Ersoy (Mimar Sinan Guzel Sanatlar Universitesi)
67. Kubra Dolaslan (Orta Dogu Teknik Universitesi)
68. Kubra Gul (Ataturk Universitesi)
69. Laurence Barker (Bilkent Universitesi)
70. Leyla Bugay (Cukurova Universitesi)
71. Lohans De Oliveira Miranda (Federal University Of Piaui)
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72. Lossian Barbosa Bacelar Miranda (Federal Institute Of Edu-cation, Science And Technology Of Piauı)
73. M. Pınar Eoglu (Dokuz Eylul Universitesi)
74. Mahmut Kuzucuoglu (Orta Dogu Teknik Universitesi)
75. Matteo Paganin (Sabancı Universitesi)
76. Meryem Sevgi Comert (Gazi Universitesi)
77. Mesut Sahin (Hacettepe Universitesi)
78. Murat Celik (Canakkale Onsekiz Mart Universitesi)
79. Murat Sahin (Ankara Universitesi)
80. Mustafa Kemal Berktas (Usak Universitesi)
81. Naime Ekici (Cukurova Universitesi)
82. Neslihan Girgin (Mimar Sinan Guzel Sanatlar Universitesi)
83. Neset Deniz Turgay
84. Nihal Gumusbas (Akdeniz Universitesi)
85. Nil Mansuroglu (Ahi Evran Universitesi)
86. Nil Orhan Ertas (Karabuk Universitesi)
87. Nurhan Sokmez (MEB)
88. Oladiti Abduljeleel Olatunji (Oluyole Local Government)
89. Olcay Coskun (Bogazici Universitesi)
90. Onur M. Orun (Bilkent Universitesi)
91. Otto Kegel
92. Omer Kusmus (Yuzuncu Yıl Universitesi)
93. Ozlem Beyarslan (Bogazici Universitesi)
94. Peter Plaumann (FAU Erlangen-Nurnberg)
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95. Pınar Comak (Orta Dogu Teknik Universitesi)
96. Pınar Ugurlu (Istanbul Bilgi Universitesi)
97. Piotr Kowalski (Uniwersytet Wroclawski)
98. Roghayeh Hafezıeh (Gebze Teknik Universitesi)
99. Samet Memis (Canakkale Onsekiz Mart Universitesi)
100. Sebnem Yıldız (Ahi Evran Universitesi)
101. Selcuk Topal (Ege Universitesi )
102. Semih Yılmaz (Kırıkkale Universitesi)
103. Serdar Enginoglu (Canakkale Onsekiz Mart Universitesi)
104. Serge Randriambololona (Galatasaray Universitesi)
105. Serkan Aydın (Ege Universitesi)
106. Sevgi Demircioglu (Canakkale Onsekiz Mart Universitesi)
107. Seyma Bodur (Orta Dogu Teknik Universitesi)
108. Sezen Bostan (Orta Dogu Teknik Universitesi)
109. Shizuo Kajı (Yamaguchi University)
110. Simon Thomas (Rutgers University)
111. Sumbul Yılmaz (Gazi Universitesi)
112. Sehmus Fındık (Cukurova Universitesi)
113. Sukru Yalcınkaya (Istanbul Universitesi)
114. Taylan Pehlivan (Ege Universitesi)
115. Tekgul Kalaycı (Sabancı Universitesi)
116. Tuba Cakmak (Ataturk Universitesi)
117. Tuba Tas (Cukurova Universitesi )
118. Tugba Yıldırım (Istanbul Teknik Universitesi)
119. Tugce Guler (Mugla Sıtkı Kocman Universitesi)
120. Tuna Altınel (Universite Claude Bernard Lyon-1)
121. Ugur Odabası (Istanbul Universitesi)
122. Ugur Ustaoglu (Abant Izzet Baysal Universitesi)
123. Ummahan Acar (Mugla Sıtkı Kocman Universitesi)
124. Vladimir Tolstykh (Arel Universitesi)
125. Yıldırım Akbal (Bilkent Universitesi)
126. Yousef Zamani (Sahand University Of Technology)
127. Yusuf Danısman (Mevlana Universitesi)
128. Zehra Velioglu (Harran Universitesi)
129. Zekiye Eser (Zirve Universitesi)
130. Zerrin Esmerligil (Cukurova Universitesi)
131. Zeynep Karaca (Ege Universitesi)
132. Zeynep Ozkurt (Cukurova Universitesi)
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Antalya Algebra Days XVII Committees
Scientific Committee
1. Feza Arslan (Mimar Sinan Guzel Sanatlar Universitesi)
2. Ayse Berkman (Mimar Sinan Guzel Sanatlar Universitesi)
3. Rostislav Grigorchuk (Texas A&M University)
4. Wolfgang Herfort ( TU Wien)
5. Piotr Kowalski (Wroclaw University)
6. Mercede Maj (Universita degli studi di Salerno)
7. Cheryl Praeger (The University of Western Australia)
8. Sinan Sertoz (Bilkent Universitesi)
9. Alev Topuzoglu (Sabancı Universitesi)
Special Session Coordinators
Algebraic Geometry: Feza Arslan (MSGSU)
Combinatorics: Alain Plagne (CMLS, Ecole polytechnique)
Group Theory: Mahmut Kuzucuoglu (ODTU)
Logic: Piotr Kowalski (Wroclaw U.), Pınar Ugurlu (Bilgi U.)
Non Associative Algebras: Naime Ekici (Cukurova U.)
Number Theory: Hamza Yesilyurt (Bilkent U.)
Rings & Modules: Nil Orhan Ertas (Karabuk U.)
Other: Ipek Tuvay (Gebze Teknik U.)
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Organizing Committee
1. Feza Arslan (Mimar Sinan Guzel Sanatlar Universitesi)
2. Gokhan Benli (ODTU)
3. Ayse Berkman (Mimar Sinan Guzel Sanatlar Universitesi)
4. Kıvanc Ersoy (Mimar Sinan Guzel Sanatlar Universitesi)
5. David Pierce (Mimar Sinan Guzel Sanatlar Universitesi)
6. Ipek Tuvay (Gebze Teknik Universitesi)