Engin Mermut

Meltem Güllüsaç, Hikmet Burak Özcan and Sedef Taşkın, Dokuz Eylül University.
Date: 2nd of August, 2017, Wednesday, Time: 09:30 – 17:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: We shall present three proofs of the Wedderburn-Artin Theorem. In the first proof for non-unital rings, we follow Szele’s article [1], firstly proving the Density Theorem. In the second proof for unital rings, we follow Nicholson’s article [2]. Both of these proofs are for semiprime right or left artinian rings. In the third proof, we follow Section 3 Structure of Semisimple Rings from the book [3] by Lam. All proofs are elementary.
References
[1] Szele, T., Simple proof of the Wedderburn-Artin structure theorem, Acta Mathematica Hungarica, 5(1-2), 101-107, 1954.
[2] Nicholson, W. K., A Short Proof of the Wedderburn Artin Theorem, New Zealand Journal of Mathematics, 22, 83-86, 1993.
[3] Lam, T. Y. A First Course in Noncommutative Rings. 2nd edition. Springer, 2001.

Meltem Güllüsaç, Dokuz Eylül University.
Date: 21st of June, 2017, Wednesday, Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: We shall make an introduction to simple rings and central algebras. See the first chapter of the book by Matej Brešar.
References
[1] Matej Brešar, Introduction to Noncommutative Algebras, Springer, 2014.

Hikmet Burak Özcan, Dokuz Eylül University.
Date: 14th of June, 2017, Wednesday, Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: We shall make an introduction to finite dimensional algebras over a field starting from finite dimensional division algebras. See the first chapters of the  book by Matej Brešar.
References
[1] Matej Brešar, Introduction to Noncommutative Algebras, Springer, 2014.

Tuğba Güroğlu, Celal Bayar University.
Date: 24th and 31st of May, and 7th of June, 2017, Wednesday, Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: Let E denote a directed graph and K be a field. The Leavitt path algebra of E with coefficient in K, denoted by L_K(E), were introduced by G. Abrams and G. Aranda Pino in 2005 as a generalization of Leavitt algebras and then extended to arbitrary graphs in 2008. In this talk, we talk about Leavitt path algebras and determine Leavitt path algebras of some graphs. Then using graph-theoretic properties, we mention the some ring-theoretic properties of Leavitt path algebras.
References
[1] Abrams, G. and Aranda Pino, G., The Leavitt path algebra of a graph, J. Algebra, 293(2), 319-334, 2005.
[2] Abrams, G. and Aranda Pino, G., The Leavitt path algebras of arbitrary graphs, Houston J. Math., 34(2), 423-442, 2008.

Haydar Göral, Koç University.
Date: 17th of May, 2017, Wednesday, Time: 11:00 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In this talk, we first define the height function and the Mahler measure from Diophantine geometry on the field of algebraic numbers. The height function measures the arithmetic complexity of an algebraic number and it has some nice properties. Then, we explain nonstandard analysis which we apply to find certain height bounds. Nonstandard analysis was originated in the 1960’s by the work of A. Robinson, which arose as a rigorous and exhaustive way of studying infinitesimal calculus. Combining the properties of the height function with ideas from model theory and nonstandard analysis, we explain how to obtain some uniform height bounds in the polynomial ring over the field of algebraic numbers. This enables us to test the primality of an ideal.

Tuğba Güroğlu, Celal Bayar University.
Date: 3rd of May, 2017, Wednesday, Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

M. Pınar Eroğlu, Dokuz Eylül University.
Date: 26th of April, 2017, Wednesday, Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206

Tuğba Güroğlu, Celal Bayar University.
Date: 29th of March, 5th, 12th and 19th of April, 2017,  Wednesday, Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

M. Pınar Eroğlu, Dokuz Eylül University.
Date: 8th and 22nd of February, 8th of March, 26th of April, 2017, Wednesday, Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: See the monograph by Beidar and Martindale and Mikhalev (Rings with generalized identities)

Selçuk Demir, Dokuz Eylül University.
Date: 25th of January, 1st and 15th of February, 1st, 15th and 22nd of March, 2017, Wednesday, Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: The aim is to obtain the Gelfand-Naimark Theorem for C*-algebras. We firstly see commutative C*-algebras and finite-dimensional C*-algebras. All the necessary functional analysis topics will be reviewed by giving the essential ideas. See also the monographs by Goodearl (Notes on Real and Complex C*-algebras) and Davidson (C*-algebras by Example).