Reverse Order Law for the Group Inverse in Semigroups and Rings

Author： Mary X.  

Publisher： Taylor & Francis Ltd

E-ISSN： 1532-4125|43|6|2492-2508

ISSN： 0092-7872

Source： Communications in Algebra, Vol.43, Iss.6, 2015-06, pp. : 2492-2508

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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 #.

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