The(b,c)-inverse in semigroups and rings with involution  

作　　者：Xiaofeng CHEN Jianlong 

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

出　　处：《Frontiers of Mathematics in China》2020年第6期1089-1104,共16页中国高等学校学术文摘·数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11771076,11871145);the Fundamental Research Funds for the Central Universities;the Postgraduate Research&:Practice Innovation Program of Jiangsu Province(No.KYCX19-0055).

摘　　要：We first prove that if a is both left(6,c)-invertible and left(c,b)-invertible,then a is both(6,c)-invertible and(c,6)-invertible in a*-monoid,which generalizes the recent result about the inverse along an element by L.Wang and D.Mosic[Linear Multilinear Algebra,Doi.org/10.1080/03081087.2019.1679073],under the conditions(a6)*=ab and(ac)*=ac.In addition,we consider that ba is(c,fe)-invertible,and at the same time ca is(6,c)-invertible under the same conditions,which extend the related results about Moore-Penrose inverses studied by J.Chen,H.Zou,H.Zhu,and P.Patricio[Mediterr J.Math.,2017,14:208]to(6,c)-inverses.As applications,we obtain that under condition(a2)^(*)=a^(2),a is an EP element if and only if a is one-sided core invertible,if and only if a is group invertible.

关 键 词：(6 c)-inverse inverse along an element core inverse EP element 

分 类 号：O15[理学—数学]