Generalized Cline's formula and Jacobson's lemma in a ring
Abstract
We present new generalized Cline's formula and Jacobson's lemma for the g-Drazin inverse in a ring. These extend many known results, e.g., Chen and Abdolyousefi (Generalized Jacobson's Lemma in a Banach algebra, Comm. Algebra, 49(2021), 3263--3272), Yan and Zeng (The generalized inverses of the products of two elements in a ring, Turk. J. Math., 44(2020), 1744--1756).
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