JORDAN DERIVATIONS ON LIE IDEALS OF PRIME AND SEMIPRIME RINGS

Abstract

We prove the following theorem: Let R ba a 2-torsion free semiprime 2

ringandUaLieidealofRsuchthatu ∈Uforallu∈U. Ifisan 2′′′′

additive mapping of R into itself satisfying (u ) = u u + uu and u ∈ U ′′′

forallu∈Uthen(uv) =uv+uv forallu,v∈U. Wealsogivea short and elementary proof of a theorem of Awtar [1] which extends a well known result of Herstein [5] on Lie ideals.