Abstract
Abstract The purpose of this paper is to study the commutativity of a prime ring ℛ {\mathscr{R}} with anti-automorphism ψ and generalized derivation ( ℱ , ξ ) {(\mathscr{F},\xi)} satisfying certain algebraic identities. Furthermore, we describe the structure of any additive map which is ψ-centralizing on a 2-torsion free prime ring with anti-automorphism ψ. We also provide examples to show that various conditions imposed on the hypotheses of our results are essential.
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