Generalized Skew Derivations and g-Lie Derivations of Prime Rings

Let R be a prime ring of characteristic different from 2, Q(r) its right Martindale quotient ring andC its extended centroid. Suppose that F is a nonzero generalized skewderivation of R, with the associated automorphisma alpha, and p(x(1), ..., x(n)) a noncentral polynomial over C, such that F([x, y]) = [F(x), alpha(y)] + [alpha(x), F(y)] for all x, y. is an element of{p( r(1), ..., r(n)) : r1, ..., r(n) is an element of R}. Then a is the identity map on R and F is an ordinary derivation of R.