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arXiv · 1706.07775

Existence criteria and expressions of the (b,c)-inverse in rings and its applications

Sanzhang Xu·Julio Benitez
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Abstract

Existence criteria for the $(b,c)$-inverse are given.% in terms of annihilators. We present explicit expressions for the $(b,c)$-inverse by using inner inverses. We answer the question when the $(b,c)$-inverse of $a\in R$ is an inner inverse of $a$. As applications, we give a unified theory of some well-known results of the $\{1,3\}$-inverse, the $\{1,4\}$-inverse, the Moore-Penrose inverse, the group inverse and the core inverse.

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Sanzhang Xu, Julio Benitez. 2017-06-23. Existence criteria and expressions of the (b,c)-inverse in rings and its applications. https://arxiv.org/abs/1706.07775

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