An Identity on -Centralizers of Lie Ideals in Prime Rings

Abstract

ABSTRACTThe main result: Let R be a 2-tortion free prime ring, U a square closed Lie ideal of R, and let T,: RR are additive mappings. Suppose that T(xyx) = q)x)T(y)q)x) holds for all pairs x,y  U. In this case T(xy) = T(x)q)y) = q)x)T(y) for all x,y  U, where  is a surjective endomorphism of U, and T(u) U, for all uU .