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

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.

Cited by in corpus (3)

• One-sided $(b,c)$-inverses in rings
• Existence criteria and expressions of the (b,c)-inverse in rings and its applications
• The reverse order law of the $(b,c)$-inverse in rings