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Reverse Order Law for the Group Inverse in Semigroups and Rings
Authors:X. Mary
Affiliation:1. Université Paris-Ouest Nanterre–La Défense , Laboratoire Modal'X , Nanterre , France xavier.mary@u-paris10.fr
Abstract:In this paper, we provide equivalent conditions for the two-sided reverse order law for the group inverse (ab)# = b # a # and (ba)# = a # b #, in semigroups and rings. Moreover, we prove that, under finiteness conditions, these conditions are also equivalent with the one-sided reverse order law (ab)# = b # a #.
Keywords:Dedekind finite ring  Finiteness conditions  Green's relations  Group inverse  Reverse order law
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