Note on derivations of semiprime rings

Abstract

Let Rbe a 2-torsion free semiprime ring with extended centroid C. For a derivation δ of Rdenote by C δthe constants of δ on C. We prove that if is a derivation of RC, where ø(X) ϵ C4 δ[X 2], then ø(δ) = 0. As an immediate consequence, we present a short proof of Ye and Luh’s theorem for arbitrary 2-torsion free semiprime rings.