Topologically semisimple topological rings

Speaker
Leonid Positselski
Date
07/05/2019 - 16:00 - 14:10Add to Calendar 2019-05-07 14:10:00 2019-05-07 16:00:00 Topologically semisimple topological rings The classical Wedderburn-Artin theorem describes associative rings A for which the category of A-modules is semisimple. This turns out to be a left-right symmetric property: the category of left A-modules is semisimple if and only if the category of right A-modules is. In this talk, I will present a generalization of the Wedderburn-Artin theory to topololgical associative rings R in which open right ideals form a base of neighborhoods of zero. The talk will start with a discussion of split and semisimple abelian categories and end with a description of topological rings R for which the category of left R-contramodules is split (or equivalently, semisimple) or, equivalently, the category of discrete right R-modules is split (or equivalently, semisimple). Building 216, Room 201 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Building 216, Room 201
Abstract

The classical Wedderburn-Artin theorem describes associative rings A for which the category of A-modules is semisimple. This turns out to be a left-right symmetric property: the category of left A-modules is semisimple if and only if the category of right A-modules is. In this talk, I will present a generalization of the Wedderburn-Artin theory to topololgical associative rings R in which open right ideals form a base of neighborhoods of zero. The talk will start with a discussion of split and semisimple abelian categories and end with a description of topological rings R for which the category of left R-contramodules is split (or equivalently, semisimple) or, equivalently, the category of discrete right R-modules is split (or equivalently, semisimple).

Last Updated Date : 05/05/2019