Month: September 2017

Salahattin Özdemir, Dokuz Eylül University.
Date: 27th of September, 4th and 11th of October, 2017, Wednesday. Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: We will prove the well-known result by Benson and Goodearl about flat modules over an arbitrary ring R: If a flat R-module M sits in a short exact sequence 0 → M → P → M → 0 with P projective, then M is projective. In other words, every flat periodic R-module M (of period 1) is projective. We will then talk about some of the recent generalizations of this result.

Sinem Benli, İzmir Institute of Technology.
Date: 20th of September, 2017, Wednesday. Time: 09:30-12:00
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: Firstly, we introduce the notion of primitive rings. After giving some examples and mentioning the properties of this class of rings, we shall prove the famous Jacobson Density Theorem which gives the structure of the primitive rings. Finally, we give a different proof of the fundamental Wedderburn’s structure theorem that characterizes the finite dimensional simple algebras.
References:
[1] Matej Brešar, Introduction to Noncommutative Algebra, Springer, 2014.
[2] Benson Farb & R. Keith Dennis, Noncommutative Algebra, Springer, 1991.