Reverse Order Law for the Group Inverse in Semigroups and Rings
Xavier Mary · Communications in Algebra · 2015
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 #.