Generalized skew derivations as a generalization of left Jordan multipliers in prime rings

Abstract

Let m, n be two nonzero fixed positive integers, R a prime ring with the right Martindale quotient ring Q, G and H two generalized skew derivations of R with the same associated automorphism α of R. If G ( x m + n ) = H ( x m ) x n is an identity for R, then either R is commutative or there exists q ∈ Q such that G ( x ) = H ( x ) = q x , for any x ∈ R .