报 告 人：Pedro Patricio 教授

工作单位：University of Minho

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.

报告一: The Moore-Penrose inverse of von Neumann regular matrices （1）

报告时间：2023年2月14日14：00-15：30

报告地点：腾讯会议：660-560-244

报告简介：In this talk, I will present necessary and sufficient conditions for a von Neumann regular matrix A over an arbitrary ring, and also the matrices arising in certain factorizations of A be Moore-Penrose invertible.

报告二: The Moore-Penrose inverse of von Neumann regular matrices （2）

报告时间：2023年2月15日14：00-15：30

报告地点：腾讯会议：872-777-894

报告简介：In this talk, I will present necessary and sufficient conditions for a von Neumann regular matrix A over an arbitrary ring, and also the matrices arising in certain factorizations of A be Moore-Penrose invertible.

报告三: The Moore-Penrose inverse of a factorization

报告时间：2023年2月16日

报告地点：腾讯会议：207-581-733

报告简介：We will present necessary and sufficient conditions for the product of matrices PAQ to be Moore-Penrose invertible, where A is von Neumann regular and there exist P and Q such that P’PA=A=AQQ’. Finally, an application is given to matrices over separative regular rings.

报告四: The inverse along an element (1)

报告时间：2023年2月18日14：00-15：30

报告地点：腾讯会议：110-111-122

报告简介：We give several criteria for the inverse along an element in rings

报告五: The inverse along an element (2)

报告时间：2023年2月19日14：00-15：30

报告地点：腾讯会议：841-842-530

报告简介：We give several criteria for the inverse along an element in rings

报告六: Some additive results on MP inverses

报告时间：2023年2月20日14：00-15：30

报告地点：腾讯会议：333-618-168

报告简介：In this talk, I will present some additive results on MP inverse of a sum of MP invertible elements. Some converse results are also presented.

报告七: On the Drazin index of regular elements

报告时间：2023年2月21日14：00-15：30

报告地点：腾讯会议：274-105-982

报告简介：It is known that the existence of the group inverse a^# of a ring element a is equivalent to the invertibility of a²a^-+1-aa^-, independently of the choice of the von Neumann inverse a^- of a. We then relate the Drazin index of a to the Drazin index of a²a^-+1-aa^-. We also give an alternative characterization when considering matrices over an algebraically closed field.

报告八: Moore-Penrose invertibility in involutory rings.

报告时间：2023年2月22日14：00-15：30

报告地点：腾讯会议：317-693-557

报告简介： Given two von Neumann regular elements a, b in a general ring with an arbitrary involution, we shall present necessary and sufficient conditions to maa^†=nbb^†.  

报告九: The link between regularity and strong-pi-regularity

报告时间：2023年2月24日14：00-15：30

报告地点：腾讯会议：754-313-106

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.

报告十: The (2,2,0) group inverse problem

报告时间：2023年2月26日14：00-15：30

报告地点：腾讯会议：898-106-899

报告简介：In this talk, I will discuss the additive group problem and the existence of the group inverse of a two by two matrix.