Characterization of Weighted (b, c) Inverse of an Element in a Ring

Abstract

The notion of weighted (b, c)-inverse of an element in rings were introduced, very recently. In this paper, we further elaborate on this theory by establishing a few characterizations of this inverse and their relationships with other (v, w)-weighted (b, c)-inverses. We introduce some necessary and sufficient conditions for the existence of the hybrid (v, w)-weighted (b, c)-inverse and annihilator (v, w)-weighted (b, c)- inverse of elements in rings. In addition to this, we explore a few sufficient conditions for the reverse-order law of the annihilator (v, w)-weighted (b, c)-inverses.