Identities with Product of Generalized Skew Derivations on Multilinear Polynomials

Abstract

Let R be a prime ring of characteristic different from 2, Qr its right Martindale quotient ring, and C its extended centroid. Suppose that F, G are generalized skew derivations of R, with the same associated automorphism, and f(x1,…, xn) a noncentral multilinear polynomial over C with n noncommuting variables, such thatfor all r1,…, rn ∈ R. Then we describe all possible forms of F and G.