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Reverse order laws for Hirano inverses in rings

Reverse order laws for Hirano inverses in rings

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 = a2b, ab2=bab, ahab2=bahab, a2bbh=abbha instead of the condition ab = ba, respectively, we present some equivalent conditions of the reverse order laws …