Abstract
Let [Formula: see text] be an associative ring with an identity and suppose that [Formula: see text] satisfy [Formula: see text] If [Formula: see text] has generalized Drazin (respectively, p-Drazin, Drazin) inverse, we prove that [Formula: see text] has generalized Drazin (respectively, p-Drazin, Drazin) inverse. In particular, as applications, we obtain new common spectral property of bounded linear operators over Banach spaces.
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