Generalized Zhou inverses in rings
Abstract
We introduce and study a new class of generalized inverses in rings. An element a in a ring R has generalized Zhou inverse if there exists b∈ R such that bab=b, b∈ comm2(a), an-ab∈ J(R) for some n∈ N. We prove that a∈ R has generalized Zhou inverse if and only if there exists p=p2∈ comm2(a) such that an-p∈ J(R) for some n∈ N. Cline's formula and Jacobson's Lemma for generalized Zhou inverses are established. In particular, the Zhou inverse in a ring is characterized.
0