Reverse order laws for Hirano inverses in rings


Yinlan Chen, Honglin Zou




In this paper, various kinds of reverse order laws for the Hirano inverse are characterized in a ring with the unit 1. Under some of conditions aba = a 2 b, ab 2 = bab, a h ab 2 = ba h ab, a 2 bb h = abb h a instead of the condition ab = ba, respectively, we present some equivalent conditions of the reverse order laws for Hirano inverses,