报 告 人：Pedro Patricio 教授

工作单位：University of Minho, Portugal

举办单位：数学学院

报告人简介：Prof. Pedro Patricio received his PhD degree in Mathematics from University of Minho, Portugal in 2002. He is currently a Professor in Department of Mathematics and Applications, University of Minho. He is the Director of the CMAT-center of Mathematics, University of Minho. His research interests include generalized inverses and partial orders in rings.  He published more than 40 peer reviewed papers in leading journals including Linear Algebra Appl., Linear Multilinear Algebra, Electron. J. Linear Algebra, and J. Aust. Math. Soc. etc.

学术报告信息（一）

报告: the theory of generalized inverses （1）

报告时间：2023年11月6日 17:00-18:00

报告地点：腾讯会议：543-668-628

报告简介：In this talk, I will introduce the theory of regular elements and its applications.

学术报告信息（二）

报告: the theory of generalized inverses （2）

报告时间：2023年11月9日17:00-18:00

报告地点：腾讯会议：231-745-990

报告简介：In this talk, I will introduce the theory of regular elements and its applications.

学术报告信息（三）

报告: the theory of generalized inverses (3)

报告时间：2023年11月13日17:00-18:00

报告地点：腾讯会议：881-555-1601

报告简介：In this talk, I will introduce the theory of regular elements and its applications.

学术报告信息（四）

报告: the theory of generalized inverses (4)

报告时间：2023年11月16日17:00-18:00

报告地点：腾讯会议：881-555-1601

报告简介：In this talk, I will introduce the theory of regular elements and its applications.

学术报告信息（五）

报告: the theory of generalized inverses (5)

报告时间：2023年11月20日17:00-18:00

报告地点：腾讯会议：881-555-1601

报告简介：In this talk, I will introduce the theory of regular elements and its applications.

学术报告信息（六）

报告: the theory of generalized inverses (6)

报告时间：2023年11月23日17:00-18:00

报告地点：腾讯会议：881-555-1601

报告简介：In this talk, I will introduce the theory of regular elements and its applications.

学术报告信息（七）

报告: On the Drazin inverse of regular elements

报告时间：2023年11月27日 10:00-11:00

报告地点：B1710

报告简介： We give an alternative characterization when considering matrices over an algebraically closed field.

学术报告信息（八）

报告: Moore-Penrose inverse

报告时间：2023年11月28日10:00-11:00

报告地点：B1710

报告简介： We shall present necessary and sufficient conditions to aa^†=bb^†.  .

学术报告信息（九）

报告: regularity and strong-pi-regularity

报告时间：2023年11月30日10:00-11:00

报告地点：B1710

报告简介：I will show that if all powers of a ring element a are regular, then a is strongly pi-regular exactly when a suitable word in the powers of a and their inner inverses is a unit.

学术报告信息（十）

报告: Characterizations of Special Clean Elements and Applications

报告时间：2023年12月1日 15:00-16:00

报告地点：B1710

报告简介：We prove that special clean decompositions of a given element of a ring are in one-to-one correspondence with the set of solutions of a simple equation in a corner ring.

学术报告信息（十一）

报告: Generalized inverses and clean decompositions

报告时间：2023年12月5日15:00-16:00

报告地点：B1710

报告简介：An element a in a ring R is called clean if it is the sum of an idempotent e and a unit u. Such a clean decomposition a = e + u is said to be strongly clean if eu = ue and special clean if aR \cap eR = (0). In this paper, we prove that a is Drazin invertible if and only if there exists an idempotent e and a unit u such that a(n) = e + u is both a strongly clean decomposition and a special clean decomposition, for some positive integer n.

学术报告信息（十二）

报告: Generalized inverses and clean decompositions （2）

报告时间：2023年12月7日15:00-16:00

报告地点：B1710

报告简介：An element a in a ring R is called clean if it is the sum of an idempotent e and a unit u. Such a clean decomposition a = e + u is said to be strongly clean if eu = ue and special clean if aR \cap eR = (0). In this paper, we prove that a is Drazin invertible if and only if there exists an idempotent e and a unit u such that a(n) = e + u is both a strongly clean decomposition and a special clean decomposition, for some positive integer n.

学术报告信息（十三）

报告: Group regular elements

报告时间：2023年12月8日15:00-16:00

报告地点：B1710

报告简介：We propose different generalizations of unit-regularity of elements in general rings (non necessarily unital rings). We then study general rings for which all elements have these properties. We notably compare them with unit-regular ideals and general rings with stable range one.