时间：2024年9月30日下午15：30-16：30

地点：雁山校区理四501报告厅

报告人：唐高华

报告简介：Abstract. An element e in a ring R is called a quasi-idempotent if e2 = ke for some central unit k of R. An element a of R is called quasi-exchange if there exists an idempotent e2 = e ∈ Ra and some central unit k of R such that 1 − e ∈ R(k − a). If every element of R is quasi-exchange, then we say R is a quasi-exchange ring. The quasi-exchange ring is a joint generalization of the exchange ring and the quasi-clean ring. The properties of the quasi-exchange ring are extensively studied. The abundant examples of quasi-exchange rings states that the quasi-exchange rings is very larger than the class of exchange rings.We also use the linear equations xa − fx = 1 to characterize the quasi-exchange elements,the quasi-clean elements and strongly quasi-clean elements respectively, and then easy to prove that the quasi-exchange elements are left-right symmetric.

报告人简介：唐高华，北部湾大学党委副书记，二级教授，博士生导师，广西十百千人才，全国优秀教师，全国师德先进个人，八桂名师，广西高校教学名师，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。主要从事数学、数学教育和高等教育国际化的研究。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。主持国家自然科学基金项目4项，省部级项目10多项，发表论文150多篇，获得省级科技进步奖1项，省部级优秀教学成果奖5项。