The generalized inverses of the products of two elements in a ring
Kai Yan, Qingping Zeng · TURKISH JOURNAL OF MATHEMATICS · 2020
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.