Generalized Inverses and Units in a Unitary Ring
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.