On gs-Drazin inverses in a ring

摘要

An element a in a ring R has a gs-Drazin inverse if there exists p(2) = p is an element of comm(2)(a) such that a - p is an element of R-qnil. In this paper, we extend Cline's formula and Jacobson's Lemma for gsDrazin inverses. Various additive properties of gs-Drazin inverses are thereby obtained.