东南大学学报（英文版）2017，Vol.33Issue(2)：249-252,4.DOI:10.3969/j.issn.1003-7985.2017.02.020
环上EP元、正规元和对称元的广义逆刻画
Characterizations of EP,normal and Hermitian elements in rings using generalized inverses
摘要
Abstract
The properties and some equivalent characterizations of equal projection(EP),normal and Hermitian elements in a ring are studied by the generalized inverse theory.Some equivalent conditions that an element is EP under the existence of core inverses are proposed.Let a∈R,then a is EP if and only if aaa#=a#aa.At the same time,the equivalent characterizations of a regular element to be EP are discussed.Let a∈R,then there exist b∈R such that a=aba and a is EP if and only if a∈R,a=aba.Similarly,some equivalent conditions that an element is normal under the existence of core inverses are proposed.Let a∈R,then a is normal if and only if a(#)a=aa(#).Also,some equivalent conditions of normal and Hermitian elements in rings with involution involving powers of their group and Moore-Penrose inverses are presented.Let a∈R(#)∩R#,n∈N,then a is normal if and only if a(#)a(a#)n=a#a(#)(a)n.The results generalize the conclusions of Mosi et al.关键词
EP元/正规元/对称元/核逆/Moore-Penrose逆/群逆Key words
equal projection(EP)elements/normal elements/Hermitian elements/core inverse/Moore-Penrose inverse/group inverse分类
数理科学引用本文复制引用
马一琳,陈建龙,韩瑞珠..环上EP元、正规元和对称元的广义逆刻画[J].东南大学学报（英文版）,2017,33(2):249-252,4.基金项目
The National Natural Science Foundation of China(No.11371089),the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020),the Natural Science Foundation of Jiangsu Province(No.BK20141327). （No.11371089）
