Abstract
Let R be a prime ring, Q(r) be the right Martindale quotient ring and C be the extended centroid of R. If G be a nonzero generalized skew derivation of R and f(x(1), x(2), ..., x(n)) be a multilinear polynomial over C such that (G(f(x(1), x(2), ..., x(n))) - f(x(1), x(2), ..., x(n))). C for all x(1), x(2), ..., x(n). R, then either f(x(1), x(2), ..., x(n)) is central valued on R or R satisfies the standard identity s(4)(x(1), x(2), x(3), x(4)).