Derivations as Homomorphisms or Anti-homomorphisms on Lie Ideals

Let R be a 2-torsion free prime ring, Z the center of R, and U a nonzero Lie ideal of R. If d is a derivation of R which acts as a homomorphism or an anti-homomorphism on U, then either d = 0 or U . Z. This result improves a theorem of Asma, Rehman, and Shakir.