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
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Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12161049). |
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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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