Formulae for the Drazin Inverse of elements in a ring

Xiaolan Qin, Linzhang Lu

Abstract


In this paper, the additive properties of the Drazin inverse in a ring $\mathcal{R}$ are studied. Some necessary and sufficient conditions for the Drazin invertible are given. Furthermore, additive formulas are derived under the conditions weaker than those used in some resent papers. The results extend those given by Wei and Deng (J.
Linear Multilinear Algebra, 59(12) (2011) 1319-1329) and Wang et al. (Filomat, 30(2016), 1185-1193).


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