Right $c$-Group Inverses and Their Applications
Received:December 09, 2021  Revised:May 08, 2022
Key Words: right $c$-group inverse   group inverse   right $c$-regular elements   strongly clean decomposition  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12161049).
Author NameAffiliation
Jun JIAO School of Mathematics and Physics, Anhui University of Technology, Anhui 243032, P. R. China 
Liang ZHAO School of Mathematics and Physics, Anhui University of Technology, Anhui 243032, P. R. China 
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Abstract:
      We study a new class of group inverses determined by right $c$-regular elements. The new concept of right $c$-group inverses is introduced and studied. It is shown that every right $c$-group invertible element is group invertible, and an example is given to show that group invertible elements need not be right $c$-group invertible. The conditions that right $c$-group invertible elements are precisely group invertible elements are investigated. We also study the strongly clean decompositions of right $c$-group invertible elements. As applications, we give some new characterizations of abelian rings and directly finite rings from the point of view of right $c$-group inverses.
Citation:
DOI:10.3770/j.issn:2095-2651.2023.01.007
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