Characterization of weighted (b,c) inverse of an element in a ring

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