GS-DRAZIN INVERSES OF GENERALIZED MATRICES OVER LOCAL RINGS

Abstract

An element $a$ in a ring $R$ has gs-Drazin inverse if there exists $b\in comm^2(a)$ such that $b=b^2a, a-ab\in R^{qnil}$.
For any $s\in C(R)$, we completely determine when a generalized matrix $A\in K_s(R)$ over a local ring $R$ has gs-Drazin inverse.