Characterization of weighted (b,c) inverse of an element in a ring
Bibekananda Sitha, Jajati Keshari Sahoo, Ratikanta Behera · Filomat · 2022
The notion of the 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 discuss a few necessary and sufficient conditions for the existence of the hybrid (v,w)-weighted (b,c)-inverse and the annihilator (v,w)-weighted (b, c)-inverse of an element in a ring. In addition, we explore a few sufficient conditions for the reverse-order law of the annihilator (v,w)-weighted (b,c)-inverses.