2022 – Dokuz Eylül University Faculty of Science Department of Mathematics

On coGalois Groups

December 26 2022December 26 2022 by Zübeyir Türkoğlu

Canan Özeren, Dokuz Eylül University.
Date: 26th of December, 2022, Tuesday, Time: 13:30 – 15:30.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

Abstract:Torsion-free covers exist for abelian groups (see [1]).
The coGalois group of a torsion-free cover $\phi: T \rightarrow A$ of an abelian group is defined in [2] as the group of $f: T \rightarrow T$ s.t. $\phi f= \phi$ and is denoted by $G(\phi)$ .
The abelian groups for which the coGalois group is trivial characterized in [3].
The notion of coGalois group can be defined in any category where we have a covering class.
In [4], coGalois groups are studied in the category of representation of quiver $q_2 : \cdot \rightarrow \cdot$ .
We talk about the necessary conditions, give in [4], the coGalois group, associated to torsion free-cover, for an object in $(q_2, Z-mod)$ .

References

[1] E. Enochs: Torsion-free covering modules. (1963)

[2] E. Enochs, J. R. García Rozas and L. Oyonarte: Compact coGalois groups. (2000).

[3] E. Enochs and J. Rada: Abelian groups which have trivial absolute \ coGalois group. (2005).

[4] Paul Hill, Abelian group pairs having a trivial coGalois Group. (2006).

2022-2023 Fall Semester Make-up Exam Schedule

December 23 2022December 20 2022 by cem çelik

Tuesday 20, December 2022	13.00	MAT 2039 Differential Equations I MAT 1015 Technical English I MAT 3059 Numerical Analysis I	Place: Head of Department Office
Wednesday 21, December 2022	10.20	MAT 1031 Calculus I MAT 1035 Analytic Geometry MAT 3055 Algebra I MAT 4045 Galois Theory	Place: Head of Department Office
Wednesday 21, December 2022	13.00	TDL 1001 Turkish Language I	Place: Head of Department Office

Coxeter Functors and Gabriel’s Theorem III

January 10 2023December 14 2022 by Zübeyir Türkoğlu

İrem Yıldız, Dokuz Eylül University.
Date: 20th of December, 2022, Tuesday, Time: 13:30 – 15:30.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

Abstract: In this talk, we will introduce the basics of representation of quivers. We will define some functors which annihilate simples and carry indecomposables to indecomposables, which will help to prove Gabriel’s Theorem that states which types of quivers have finitely many isomorphisms classes of indecomposable representations.

References

[1] Some lecture notes in Bielefeld university from Henning Krause .

[2] Article from I. N. Bernstein, I. M. Gel’fand, V. A. Ponomarev named “Coxeter functor and Gabriel ‘s theorem”.

Coxeter Functors and Gabriel’s Theorem II

December 13 2022December 13 2022 by Zübeyir Türkoğlu

İrem Yıldız, Dokuz Eylül University.
Date: 13th of December, 2022, Tuesday, Time: 13:30 – 15:30.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

References

[1] Some lecture notes in Bielefeld university from Henning Krause .

[2] Article from I. N. Bernstein, I. M. Gel’fand, V. A. Ponomarev named “Coxeter functor and Gabriel ‘s theorem”.

Coxeter Functors and Gabriel’s Theorem

December 5 2022December 5 2022 by Zübeyir Türkoğlu

İrem Yıldız, Dokuz Eylül University.
Date: 6th of December, 2022, Tuesday, Time: 13:30 – 15:30.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

References

[1] Some lecture notes in Bielefeld university from Henning Krause .

[2] Article from I. N. Bernstein, I. M. Gel’fand, V. A. Ponomarev named “Coxeter functor and Gabriel ‘s theorem”.

The Existence of Almost Split Sequences

November 29 2022November 29 2022 by Zübeyir Türkoğlu

Fatma Kaynarca, Afyon Kocatepe University.
Date: 29th of November, 2022, Tuesday, Time: 13.00 – 16.30.
Place: Online-Sakai-Graduate Meetings

Abstract: In this seminar, the existence of almost split sequences in the category of modules built on a finite-dimensional algebra will be proved with a functorial approach.

On Higher Commutators

November 22 2022November 22 2022 by Zübeyir Türkoğlu

M. Pınar Eroğlu, Dokuz Eylül University.
Date: 25th of October, 2022, Tuesday, Time: 13:30 - 15:30.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract:  A general result on higher commutators due to Herstein I.N. states that if A is a noncommutative simple algebra over a field of characteristic not 2, then the only higher commutators of A are A and [A,A]. For a more general approach, the question that arises naturally is: Which assumptions should be required to obtain a result similar to above in the case where A is an arbitrary noncommutative unital algebra? In this talk, we characterize higher commutators of unital algebras discussing the question above.

Almost Split and Minimal Morphisms

November 21 2022November 21 2022 by Zübeyir Türkoğlu

Fatma Kaynarca, Afyon Kocatepe University.
Date: 21th of November, 2022, Tuesday, Time: 13.00 – 16.30.
Place: Online-Sakai-Graduate Meetings

Abstract: In this seminar, almost split morphisms, another concept that use to characterize almost split sequences, will be introduced and their relationship to irreducible morphisms and minimal morphisms will be examined.

Almost Split Sequences

November 14 2022November 14 2022 by Zübeyir Türkoğlu

Fatma Kaynarca, Afyon Kocatepe University.
Date: 15th of November, 2022, Tuesday, Time: 13.00 – 14.00.
Place: Online-Sakai-Graduate Meetings

Abstract: Almost split sequences arose from an attempt to understand the morphisms lying in the radical of a module category are minimal non-split short exact sequences. This sequences were introduced by Maurice Auslander and Idun Reitenin 1974-1975 and have become a central tool in the theory of representations of finite dimensional algebras. We start our discussion in seminar with a short description of the radical of a module category. Then we will define and study irreducible morphisms, almost split morphisms, minimal morphisms, almost split sequences and also give some characterizations of these notions.

34. Ulusal Matematik Sempozyumu

November 8 2022November 8 2022 by cem çelik

Ulusal Matematik Sempozyumlarının 34’üncüsü, Türk Matematik Derneğinin desteği ile Dokuz Eylül Üniversitesi Matematik Bölümünde, 31 Ağustos-3 Eylül 2022 tarihleri arasında yüzyüze gerçekleştirilecektir. 1988 yılından beri gerçekleştirilen Ulusal Matematik Sempozyumlarının programı, genel konuşma, çağrılı ana konuşmalar, dizi konuşmalar ve genç araştırmacı konuşmaları, kısa konuşmalar ve poster sunumlarından oluşmaktadır.

İzmir’in kurtuluşunun 100. yılında sizleri ağırlamaktan gurur ve mutluluk duyacağız.

https://math.deu.edu.tr/ums2022/