One-sided $(b,c)$-inverses in rings

Abstract

In this paper we introduce a new generalized inverse in a ring -- one-sided $(b,c)$-inverse, derived as an extension of $(b,c)$-inverse. This inverse also generalizes one-sided inverse along an element, which was recently introduced by H. H. Zhu et al. [H. H. Zhu, J. L. Chen, P. Patrício, Further results on the inverse along an element in semigroups and rings, Linear Multilinear Algebra, 64 (3) (2016) 393-403]. Also, here we present one-sided annihilator $(b,c)$-inverse, which is an extension of the annihilator $(b,c)$-inverse. Necessary and sufficient conditions for the existence of these new generalized inverses are obtained. Furthermore, we investigate conditions for the existence of one-sided $(b,c)$-inverse of a product of three elements and we consider some properties of one-sided $(b,c)$-inverses.

References in corpus (1)

• Characterizations of the $(b,c)$-inverse in a ring

Cited by in corpus (2)

• Existence criteria and expressions of the (b,c)-inverse in rings and its applications
• Characterizations of annihilator $(b,c)$-inverses in arbitrary rings