The generalized inverses of the products of two elements in a ring

Authors: KAI YAN, QINGPING ZENG

Abstract: In this paper, new extensions of Jacobson's lemma and Cline's formula for Drazin inverses, generalized Drazin inverses, and ($m,n$)-pseudo-inverses are given. As applications, we provide a formula for the powers of the products of two elements and establish connections between two B-Fredholm elements through the canonical map.

Keywords: Drazin inverses, generalized Drazin inverses, ($m,n$)-pseudo-inverses, Jacobson's lemma, Cline's formula

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