On G-Drazin partial order in rings

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