报告题目： Products of Idempotents
报告人： André Leroy教授
报告时间：2025年05月23日（星期五）下午15:30-16:30
报告地点：藕舫楼724室
主持人： 王尧教授
报告摘要：For various reasons, idempotents are of central importance in algebra.Decomposing elements into a product of idempotents is a natural quest.Howie proved in the 60's that any non-bijective map from a finite set to itself is a product of idempotent maps. Erdos, Laffey, Ruytenburg extended the decomposition of a singular matrix into a product of idempotent matrices over fields, division rings, Bézout domains. Since von Neumann rings have plenty of idempotent elements, it is natural to ask the question for this class of rings. Hannah and O'Meara obtained very interesting results in this area.
In this talk I'll first present a short history of the problem and consider the question for singular matrices over classes of noncommutative rings (right Bézout domain, quasi Euclidean rings,...) I will also connect the question with various properties of rings. I will end the talk discussing connections with a longstanding open question in von Neumann regular rings.
报告人简介：André Leroy教授是法国阿尔图瓦大学荣誉教授。在Ore扩张的素理想结构、同态映射及Goldie条件等领域发表了奠基性论文；提出并发展了奇异矩阵分解为幂等矩阵的系列理论，应用于线性代数与环论；发表80篇以上高水平论文，多篇发表于《Journal of Algebra》《Linear Algebra and Its Applications》等顶级期刊；担任《Journal of Algebra and Its Applications》等期刊编委。
欢迎广大师生踊跃参加！
数学与统计学院
江苏省应用数学（南京信息工程大学）中心
江苏省系统建模与数据分析国际合作联合实验室
江苏省统计科学研究基地
2025年5月20日
