COMMUTING MAPS ON LIE IDEALS

Let R be a ring and let A be a subset of R. A map f : A --> R is commu ting on A if [f(x), x] = 0 for all x is an element of A where [x, y] = xy - yx. Suppose that R is a prime ring of characteristic not equal 2 with extended centroid C. If L is a noncommutative Lie ideal of R and f : L --> R an additive commuting map, then there is lambda is an ele ment of C and an additive map xi : L --> C such that f(nu) = lambda nu + xi(nu) for all nu is an element of L.