Reverse Order Law for the Core Inverse in Rings

Abstract

In this paper, necessary and sufficient conditions of the onesided reverse order law (ab)((sic)) = b((sic))a((sic)) , the two-sided reverse order law (ab)((sic)) = b((sic))a((sic)) and (ba)((sic)) = a((sic))b((sic)) for the core inverse are given in rings with involution. In addition, the mixed-type reverse order laws, such as (ab)((sic)) = b((sic))(abb((sic)))((sic)) , a((sic)) = b(ab)((sic)) and (ab)((sic)) = b((sic)) a((sic)) , are also considered.