报告题目：Generalized inverses and units in a unitary ring
报告人：陈建龙
报告人单位：东南大学数学学院
报告时间：2024年6月13日（星期四）10:00
报告地点：教2-327
主办单位：BETVLCTOR伟德官网app下载
邀请人：应志领
报告内容：
Let R be a unitary ring and $a,b \in R$ with $ab = 0$. We find the 2/3 propert of Drazin invertibility: if any two of $ a, b$ and $a + b$ are Drazin invertible, then so is the third one. Then, we combine the 2/3 property of Drazin invertibility to characterize the existence of generalized inverses by means of units. As applications, the need for two invertible elements used by You and Chen to characterize the group invertibility of a sum of morphisms is reduced to that for one invertible element, and the existence and expression of the inverse along a product of two regular elements are obtained, which generalizes the main result of Mary and Patrcio about the group inverse of a product.
报告人简介：陈建龙，东南大学特聘教授、二级教授，博士生导师，享受国务院政府特殊津贴，教育部大学数学课程教学指导委员会委员，中国高等教育学会教育数学专业委员会副理事长。曾任东南大学数学系主任，中国数学学会理事，江苏省数学学会副理事长。获首届全国教材建设奖---全国优秀教材二等奖，宝钢优秀教师特等奖提名奖，第四届教育部“高校青年教师奖”。主持的课程获国家级线上线下混合式一流课程，国家级线上一流课程，国家精品在线开放课程，国家精品资源共享课程，国家精品课程。作为主持人获江苏省教学成果一等奖，主持的教学团队获江苏高校优秀教学团队、江苏高校省级优秀基层教学组织，获首届全国高校大学数学课程教学创新示范交流活动一等奖、省特等奖，首届东南大学杰出教学奖之教学卓越奖。主要从事代数学的科学研究，迄今共主持7项国家自然科学基金项目，主持2项教育部博士点基金项目，已发表SCI收录论文200余篇，出版学术专著3本，曾获第四届江苏省青年科技标兵，中国高校自然科学二等奖，江苏省科学进步三等奖。
报告题目：Unit-fusible property via regularity
报告人：周毅强
报告人单位： Memorial University of Newfoundland，Canada
报告时间：2024年6月13日（星期四）10:00
报告地点：教2-327
主办单位：BETVLCTOR伟德官网app下载
邀请人：应志领
报告内容：
An element in a ring (associative with identity) is called left unit-fusible if it is the sum of a left zero-divisor and a unit, and the ring is left unit-fusible if each of its nonzero elements is left unit-fusible. These notions rose in a paper by Ghashghaei and McGovern [E. Ghashghaei and W.Wm. McGovern, Fusible rings. Comm. Algebra 45(3) (2017), 1151-1165], where, among others, it is shown that unit-regular rings are unit-fusible and a question left open asks whether or not every von Neumann regular ring is unit-fusible. In this talk, we address the question of how (unit-) regularity and unit-fusible property are related to each other.
报告人简介：Zhou is a tenured full professor in Mathematics at the Memorial University of Newfoundland, specializing in ring theory and module theory. Zhou is a co-author of the monograph ``Classes of Modules'' (Pure and Applied Mathematics, 281. Chapman and Hall/CRC, Boca Raton, FL, 2006), and the author or co-author of over 170 peer-reviewed articles. Zhou's research is funded by the Natural Sciences and Engineering Research Council of Canada. Zhou is a referee for several publishing houses such as John Wiley & Sons, Inc., Cambridge University Press and World Scientific Publishing Co., and for more than 30 periodicals including Acta Applicandae Mathematicae, Bulletin des Sciences Mathematiques, Canadian Mathematical Bulletin, Communications in Algebra, Glasgow Mathematical Journal, Journal of Algebra, Journal of Algebra and its Applications, Journal of Australian Mathematical Society, Journal of Pure and Applied Algebra, Linear Algebra and its Applications, Linear and Multilinear Algebra, Mathematische Zeitshrift, Pacific Journal of Mathematics, and the AMS Contemporary Mathematics series. Zhou is an associate editor of ``Journal of Algebra and its Applications''.