Some Results on Generalized Derivations and (σ, τ)- Lie Ideals

Let R be a prime ring with characteristic not 2 and sigma, tau, alpha,beta, lambda, mu, gamma automorphisms of R. Let h : R -> R be a nonzero left(resp.right)-generalized (alpha, beta) derivation, b is an element of R and V not equal 0 a left (sigma, tau)-Lie ideal of R. The main object in this article is to study the situations. (1) h(I) subset of C-lambda,C-mu (V), (2) bh(I) subset of C-lambda,C-mu (V) or h(I)b subset of C-lambda,C-mu(V), (3) h lambda(V) = 0, (4) h lambda(V)b = 0 or bh lambda (V) = 0.