A simple introduction to pure semisimplicity conjecture
发布人: 曹思圆   发布时间: 2022-06-06   浏览次数: 10

*时间:20220607日  10:00-11:00


*主讲人:汪军鹏 副教授

*主持人:周国栋 教授


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.


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. AlgebraJPAAC.R. Math等期刊发表论文十余篇。