Characterizations of Outer Generalized Inverses. Issue 4 (1st December 2017) - Wang, Long; Castro-Gonzalez, Nieves; Chen, Jianlong
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.