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

Long Wang; Jianlong Chen; Nieves Castro-González

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

Rings and Algebras 2015-07-07 v1

Authors: Long Wang , Jianlong Chen , Nieves Castro-González

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.

Keywords

(b,c)-inverse ring theory direct sum decomposition annihilator idempotent reverse order rule

Cite

@article{arxiv.1507.01446,
  title  = {Characterizations of the $(b, c)$-inverse in a ring},
  author = {Long Wang and Jianlong Chen and Nieves Castro-González},
  journal= {arXiv preprint arXiv:1507.01446},
  year   = {2015}
}

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