Centralizer’s applications to the (b, c)-inverses in rings

Abstract

We give several conditions in order that the absorption law for one sided (b, c)-inverses in rings holds. Also, by using centralizers, we obtain the absorption law for the (b, c)-inverse and the reverse order law of the (b, c)-inverse in rings. As applications, we obtain the related results for the inverse along an element, Moore–Penrose inverse, Drazin inverse, group inverse and core inverse.