Generalized cline's formula for the generalized Drazin inverse in rings


Huanyin Chen, Marjan Sheibani Abdolyousefi




In this paper, we present new generalized Cline's formula for g-Drazin inverse in rings and Banach algebras. These extend many known results, e.g., Chen and Abdolyousefi (Cline's formula for g-Drazin inverses in a ring, Filomat, 33(2019), 2249-2255), Miller and Zguitti (New extensions of Jacobson's lemma and Cline's formula, Rend. Circ. Mat. Palermo, II. Ser., 67(2018), 105-114).