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.
YAN, KAI and ZENG, QINGPING
"The generalized inverses of the products of two elements in a ring,"
Turkish Journal of Mathematics: Vol. 44:
5, Article 17.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss5/17