云亭数学讲坛2021第57讲——唐高华教授

 应皇冠正规娱乐平台邀请，北部湾大学唐高华教授将为皇冠正规娱乐平台师生作线上学术报告。

报告题目：Quasi-clean rings and strongly quasi-clean rings

报告摘要：An element a of a ring R is called a quasi-idempotent if a² = ka for some central unit k of R, or equivalently, a = ke, where k is a central unit and e is an idempotent of R. A ring R is called a quasi-Boolean ring if every element of R is quasi-idempotent. A ring R is called (strongly) quasi-clean if each of its elements is a sum of a quasi-idempotent and a unit (that commute). These rings are shown to be a natural generalization of the clean rings and strongly clean rings. An extensive study of (strongly) quasi-clean rings is conducted. The abundant examples of (strongly) quasi-clean rings state that the class of (strongly) quasi-clean rings is very larger than the class of (strongly) clean rings. We prove that an indecomposable commutative semilocal ring is quasi-clean if and only if it is local or R has no image isomorphic to Z₂. For an indecomposable commutative semilocal ring R with at least two maximal ideals, Mn(R)(n≥2) is strongly quasi-clean if and only if Mn(R) is quasi-clean if and only if min{∣R/m∣, m is a maximal ideal of R}>n+1. For a prime p and a positive integer n≥2, Mn(Z(p)) is strongly quasi-clean if and only if p > n. Some open questions are also posed.

报告时间：2021年10月12日19:30

报告地点：腾讯会议号 601226687

邀 请 人：乔虎生

 届时欢迎广大师生参与交流！

【报告人简介】

 唐高华，北部湾大学副校长、理学院教授，博士生导师，教育部高等学校数学类专业教学指导委员会委员，广西高校数学类专业教学指导委员会主任委员，广西数学会理事长。广西十百千人才，全国优秀教师，八桂名师，广西高校教学名师，主要从事交换代数、同调代数、环的代数结构与图结构等的研究。定义了交换环的弱Krull维数，证明了弱Krull维数为2的广义伞环上Bass-Quillen猜想成立。建立了环上形式矩阵环理论，其中的一类被称之为唐-周环。在环的内部刻画、环的同调理论、环的代数结构与图结构、环上形式矩阵环等的研究中取得了系列成果，发表论文150多篇。