One-sided $(b, c)$-inverses in rings
Abstract
In this paper we introduce a new generalized inverse in a ring -- one-sided -inverse, derived as an extension of -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. Patr\'{i}cio, 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 -inverse, which is an extension of the annihilator -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 -inverse of a product of three elements and we consider some properties of one-sided -inverses.
Cite
@article{arxiv.1607.06230,
title = {One-sided $(b, c)$-inverses in rings},
author = {Yuanyuan Ke and Jelena Višnjić and Jianlong Chen},
journal= {arXiv preprint arXiv:1607.06230},
year = {2016}
}