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arXiv · 1507.01446

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

Long Wang·Jianlong Chen·Nieves Castro-González
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Abstract

Let $R$ be a ring and $b, c\in R$. In this paper, we give some characterizations of the $(b,c)$-inverse, in terms of the direct sum decomposition, the annihilator and the invertible elements. Moreover, elements with equal $(b,c)$-idempotents related to their $(b, c)$-inverses are characterized, and the reverse order rule for the $(b,c)$-inverse is considered.

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Long Wang, Jianlong Chen, Nieves Castro-González. 2015-06-04. Characterizations of the $(b, c)$-inverse in a ring. https://arxiv.org/abs/1507.01446

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