Annihilators and Power Values of Generalized Skew Derivations on Lie Ideals

Let R be a prime ring of characteristic different from 2, let Q(r) be its right Martindale quotient ring, and let C be its extended centroid. Suppose that F is a generalized skew derivation of R, L a non-central Lie ideal of R, 0 not equal a is an element of R, m >= 0 and n, s >= 1 fixed integers. If a(u(m)F(u)u(n))(s) = 0 for all u is an element of L, then either R subset of M-2(C), the ring of 2 x 2 matrices over C, or m = 0 and there exists b is an element of Q(r), such that F(x) = bx, for any x is an element of R, with ab = 0.