Zübeyir Türkoğlu

Krull-Schmidt via the exchange property

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Victor Blasco Jimenez, Dokuz Eylül University.
Date: 8th of March, 2022, Tuesday, Time: 10.00 – 12.00.
Place: Dokuz Eylül University, Tınaztepe Campus, Faculty of Science, Department of Mathematics, room B206 (department seminar and meeting room).
Abstract: We will define what is called the exchange property and study modules for which this property holds. Later we will see how it can be used to prove the Krull-Schmidt Theorem and related ones for various classes of modules.


Artinian Serial Rings

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Noyan ER, Dokuz Eylül University.
Date: 1st of March, 2022, Tuesday, Time: 10.00 – 12.00.
Place: Dokuz Eylül University, Tınaztepe Campus, Faculty of Science, Department of Mathematics, room B206 (department seminar and meeting room).
Abstract: We will continue our discussion of serial rings giving basic information about Artinian serial rings and presenting a standard proof that they have finite representation type.

Algebraic Unit Fractions

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Haydar Göral, Dokuz Eylül University.
Date: 25th of December, 2019, Wednesday, Time: 14.45 – 16.15.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B256.
Abstract: In this talk, we consider algebraic unit fractions. We show that the finiteness of the set of all solutions of certain Diophantine equations in algebraic unit fractions determines the field of rational numbers among all real number fields.

On the Strong Degrees of Unital Rings

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M. Pınar Eroğlu, Dokuz Eylül University.
Date: 18th of December, 2019, Wednesday, Time: 14.45 – 16.15.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B256.
Abstract: In this seminar, we will first investigate the relationships between the degree of algebraicity of an element and its strong degree. And then we will continue to talk about the strong degrees of unital rings.

Multiple Zeta Values

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Burak Turfan, Dokuz Eylül University.
Date: 11th of December, 2019, Wednesday, Time: 14.45 – 16.15.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B256.
Abstract: In this talk, I will introduce Riemann zeta function and multiple zeta values. Also, We see that Euler’s formula that is values of Riemann zeta functions at the even integers. I will try to find some linear relation between Rieman zeta function and multiple zeta values. The main purpose of this talk finding algebraic relation of Q-vector spaces of R which is generated by multiple zeta values according to their weight and length, and talking about their dimensions. Finally, I will mention about some conjectures.

Frobenius Algebras, Gendo-Symmetric Algebras, Comultiplications and Dominant Dimension

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Çiğdem Yırtıcı, University of Stuttgart.
Date: 4th of December, 2019, Wednesday, Time: 14.45 – 16.15.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B256.
Abstract: Two large classes of algebras, Frobenius algebras and gendo-symmetric algebras, are characterized by comultiplication with some special properties. But, there are differences between them. The aim of this talk is to introduce the class of gendo-symmetric algebras which is constructed by Fang and König and clarify these differences.   

On the Strong Degree

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M. Pınar Eroğlu, Dokuz Eylül University.
Date: 13rd of November, 2019, Wednesday, Time: 14.45 – 16.15.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B256.
Abstract: In this seminar, we will introduce the concept of the strong degree of a unital ring. The definition involves a rather technical condition, but we shall see that the strong degree can be rather easily computed for certain classes of rings.

Reference: 1. Brešar, M., Chebotar, M. A., and Martindale, W. S. (2007). Functional identities. Springer Science & Business Media.