Weak inverses of products — Cline’s formula meets Jacobson lemma

Abstract

We study extensions of Cline’s formula and Jacobson lemma for one-sided, commuting and bicommuting weak inverses, in semigroups and general rings. In particular, we provide various isomorphisms between the (one-sided, commuting and bicommuting) weak inverses of [Formula: see text] and those of [Formula: see text] (or [Formula: see text] and [Formula: see text] when [Formula: see text] and [Formula: see text] satisfy additional identities).