March 2023 – Dokuz Eylül University Faculty of Science Department of Mathematics

On coGalois Groups II

March 27 2023March 27 2023 by Zübeyir Türkoğlu

Canan Özeren, Dokuz Eylül University.

Date: 29th of March, 2023, Wednesday,

Time: 10:30 – 12:00.

Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206 (Online-Sakai-Graduate Meetings).

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 were characterized in [3]. The notion of coGalois group can be defined in any category where we have a covering class. In [4], coGalois groups have been studied in the category of representations of the quiver $q_2 : \cdot \rightarrow \cdot$ . We talk about the necessary and sufficient conditions for coGalois group, associated to a torsion free-cover of an object in $(q_2, Z-mod)$ to be trivial.

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). [5] Molly Dukun, Phd Thesis

[5] Molly Dukun, Phd Thesis

Graduate Education in Mathematics

May 22 2024March 20 2023 by Celal Cem Sarıoğlu

Assoc. Prof. Dr. Burcu SİLINDİR YANTIR (Vice Chair), Date: 28.03.2023, Time: 16:00, Place: online.deu.edu.tr

In cooperation with Dokuz Eylül University Faculty of Science Department of Mathematics and Career Planning Center, a conversation moderated by Assist.Prof.Dr. Celal Cem SARIOĞLU and on “Graduate Education in Mathematics” will be held with Assoc. Prof. Dr. Burcu SİLİNDİR YANTIR, who is vice chair of Mathematics department. Those who are interested are asked to contact the moderator.

On Rings Whose Finite Length Indecomposable Modules Are Completely Determined by Their Composition Factors III

March 14 2023March 14 2023 by Zübeyir Türkoğlu

Victor Blasco Jimenez, Dokuz Eylül University.

Date: 15th of March, 2023, Wednesday, Time: 10.30 – 12.00.

Place:Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206 (Online-Sakai-Graduate Meetings).

Abstract: Today we will continue the discussion we started the other day. In particular, we will prove that a commutative Artinian Ring $R$ is of finite representation type if and only if it satisfies $\mathfrak{X}$ , that is, if and only if finitely generated indecomposable $R$ -modules are completely determined by their composition factors.

On Rings Whose Finite Length Indecomposable Modules Are Completely Determined by Their Composition Factors II

March 7 2023 by Zübeyir Türkoğlu

Victor Blasco Jimenez, Dokuz Eylül University. Date: 8th of March, 2023, Wednesday, Time: 10.30 – 12.00. Place:Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206 (Online-Sakai-Graduate Meetings). Abstract: Today we will continue the discussion we started the other day. In particular, we will show that a commutative Artinian Ring $R$ of finite representation type satisfies $\mathfrak{X}$ , that is, finitely generated indecomposable $R$ -modules are completely determined by their composition factors.