Characterizations of Outer Generalized Inverses

Source abstract

Abstract Let R be a ring and b , c ∊ 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.