Characterizations of weighted (b,c) inverse

10/19/2020

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by   Bibekananda Sitha, et al.

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The notion of weighted (b,c)-inverse of an element in rings were introduced, very recently [Comm. Algebra, 48 (4) (2020): 1423-1438]. 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.