Formulae for the Drazin inverse of elements in a ring

Xiaolan Qin, Linzhang Lu

This paper studies additive properties of the Drazin inverse in a ring R. Some necessary and sufficient conditions for the Drazin invertible are given. Furthermore, we derive additive formulae under conditions weaker than those used in some resent papers on the subject. These extend the main results of Wei and Deng (J. Linear Multilinear Algebra, 59(12) (2011) 1319-1329) and Wang et al. (Filomat, 30(2016), 1185-1193)