Characterizations of annihilator $(b,c)$-inverses in arbitrary rings

Abstract

In this paper, we investigate some properties of annihilator (b, c)-inverses in an arbitrary ring. We demonstrate that one-sided annihilator (b, c)-inverses of elements in arbitrary rings may behave differently in contrast to one-sided (b, c)-inverses. Also, we discuss intertwining property, absorption law, reverse order law, and Cline's formula for annihilator (b, c)-inverses. As applications, we improve and extend some known results to (b, c)-inverses. In particular, we derive an equivalent condition of intertwining property for (b, c)-inverses in semigroups.