Strong commutativity preserving maps on Lie ideals

Let A be a prime ring and let R be a noncentral Lie ideal of A. An additive map f : R -> A is called strong commutativity preserving (SCP) on R if [f(x), f(y)] = [x, y] for all x, y is an element of R. In this paper we show that if f is SCP on R, then there exist; lambda is an element of C, lambda(2) = 1 and an additive map mu : R -> L(A) such that f (x) = lambda x + mu(x) for all x is an element of R where C is the extended centroid of A, unless chan A = 2 and A satisfies the standard identity of degree 4. (c) 2007 Elsevier Inc. All rights reserved.