Extensions of Jacobson's lemma for Drazin inverses

摘要

We study the generalization of Jacobson's lemma for the group inverse, Drazin inverse, generalized Drazin inverse and pseudo Drazin inverse of 1 - bd (or 1 - ac) in a ring when 1 - ac (or 1 - bd) has a corresponding inverse, acd = dbd and bdb = bac (or dba = aca). Thus, we recover some recent results.