Strong commutativity preserving maps on Lie ideals Original Research Article

Let image be a prime ring and let image be a noncentral Lie ideal of image. An additive map image is called strong commutativity preserving (SCP) on image if [f(x),f(y)]=[x,y] for all image. In this paper we show that if f is SCP on image, then there exist image, λ2=1 and an additive map image such that f(x)=λx+μ(x) for all image where image is the extended centroid of image, unless charimage and image satisfies the standard identity of degree 4.