On G-Drazin partial order in rings

Abstract

AbstractWe extend the concept of a G-Drazin inverse from the set $$M_n$$ M n of all $$n\times n$$ n × n complex matrices to the set $$\mathcal{R}^{D}$$ R D of all Drazin invertible elements in a ring $$\mathcal{R}$$ R with identity. We also generalize a partial order induced by G-Drazin inverses from $$M_n$$ M n to the set of all regular elements in $$\mathcal{R}^{D}$$ R D , study its properties, compare it to known partial orders, and generalize some known results.