Right $c$-Group Inverses and Their Applications

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.