雲亭數學講壇2021第57講——唐高華教授

 應77779193永利邀請，北部灣大學唐高華教授将為我院師生作線上學術報告。

報告題目：Quasi-clean rings and strongly quasi-clean rings

報告摘要：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.

報告時間：2021年10月12日19:30

報告地點：騰訊會議号 601226687

邀 請 人：喬虎生

 屆時歡迎廣大師生參與交流！

【報告人簡介】

 唐高華，北部灣大學副校長、理學院教授，博士生導師，教育部高等學校數學類專業教學指導委員會委員，廣西高校數學類專業教學指導委員會主任委員，廣西數學會理事長。廣西十百千人才，全國優秀教師，八桂名師，廣西高校教學名師，主要從事交換代數、同調代數、環的代數結構與圖結構等的研究。定義了交換環的弱Krull維數，證明了弱Krull維數為2的廣義傘環上Bass-Quillen猜想成立。建立了環上形式矩陣環理論，其中的一類被稱之為唐-周環。在環的内部刻畫、環的同調理論、環的代數結構與圖結構、環上形式矩陣環等的研究中取得了系列成果，發表論文150多篇。