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 |
|
|
