The Commutativity of Prime *-Rings with Generalized Derivations

This paper studies the commutativity of unital 2-torsion-free prime rings with an involution of the second kind. We investigate several identities involving generalized derivations on such rings. Our main results are new commutativity theorems, which show that any one of the identities involving generalized derivations yields the commutativity of the underlying ring. These identities connect the derivations with the ring’s involution* through Lie or Jordan products. Our work extends many known existing results in the area.