*主持人：周国栋 教授

*讲座内容简介：
Recall that a ring R is semisimple (resp.pure semisimple) if R is both left and right semisimple (resp. pure semisimple). Here R is left semisimple (resp. left pure semisimple) if all left R-modules are projective (resp. pure projective). Equivalently, if all left R-modules are injective (resp. pure injective). right semisimple(resp.right pure semisimple) rings are defined dually. It is well known that semisimple rings are left-right symmetric, that is, a ring R is left semisimple if and only if it is right semisimple. The question whether pure semisimple rings are left-right symmetric is known as pure semisimplicity conjecture. Such a conjecture is still open and is closely related to ``global decomposition problems'', rings of finite representation type and K\"{o}the's problem.

In this talk, we will give an introduction to pure semisimplicity conjecture and some our works and ideas for such a conjecture.

This talk is a joint work with Prof. Z. K. Liu.

*主讲人简介：
汪军鹏，西北师范大学数学与统计学院副教授，2018年博士毕业，主要从事Gorenstein同调代数及三角范畴方面的研究。目前在J. Algebra、JPAA、C.R. Math等期刊发表论文十余篇。