On Jordan Left Derivations of Lie Ideals in Prime Rings

Abstract

Let R be a prime ring with characteristic different from two and U be a Lie ideal of R such that u² ɛ U for all u ɛ U. In the present paper it is shown that if d is an additive mappings of R into itself satisfying d(u²) = 2ud(u), for all u ɛ U, then either U ɛ Z(R) or d(U) = (0).