Generalized Inverses and Units in a Unitary Ring

作     者：Yu Kun ZHOU Jian Long CHEN Yu Kun ZHOU;Jian Long CHEN

作者机构：School of MathematicsSoutheast UniversityNanjing 210096P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2024年第40卷第4期

页      面：1000-1014页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.12171083,11871145,12071070) the Qing Lan Project of Jiangsu Province the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX22-0231) 

主　　题：Leftπ-regular element stronglyπ-regular element group inverse Drazin inverse inverse along an element 

摘      要：Let R be a unitary ring and a,b∈R with ab=*** find the 2/3 property of Drazin invertibility:if any two of a,b and a+b are Drazin invertible,then so is the third ***,we combine the 2/3 property of Drazin invertibility to characterize the existence of generalized inverses by means of *** applications,the need for two invertible morphisms used by You and Chen to characterize the group invertibility of a sum of morphisms is reduced to that for one invertible morphism,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 Patricio(2016)about the group inverse of a product.