Higher Derivations on Lie Ideals

In this paper we present a brief proof of a recently proved result [5, Corollary 1.4]. The main result states that if R is a prime ring of characteristic different of 2 and U is a Lie ideal of R where U 6½ Z(R), the center of R, u2 2 U for all u 2 U, and D is a Jordan higher derivation of U into R, then D is a higher derivation of U into R. This result extends a theorem of Awtar [1].