Generalized Inverses and Units in a Unitary Ring  

作　　者：Yu Kun ZHOU Jian Long CHEN 

机构地区：[1]School of Mathematics,Southeast University,Nanjing 210096,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第4期1000-1014,共15页数学学报（英文版）

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)。

摘　　要：Let R be a unitary ring and a,b∈R with ab=0.We 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 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 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.

关 键 词：Leftπ-regular element stronglyπ-regular element group inverse Drazin inverse inverse along an element 

分 类 号：O151.21[理学—数学]