IDENTITIES WITH PRODUCT OF GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS

Let R be a prime ring of characteristic different from 2, Q(r) 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(x(1), ... ,x(n)) a noncentral multilinear polynomial over C with n noncommuting variables, such that F(f(r(1),...,r(n) ))G(f(r(1),..., r(n))) = 0 for all r(1),..., r(n) is an element of R. Then we describe all possible forms of F and G.