JORDAN DERIVATIONS ON LIE IDEALS OF PRIME AND SEMIPRIME RINGS

Abstract

We prove the following theorem: Let R ba a 2-torsion free semiprime ring and U a Lie ideal of R such that u2 ∈ U for all u ∈ U. If is an additive mapping of R into itself satisfying (u2) = uu +uu and u ∈ U for all u ∈ U then (uv) = uv + uv for all u,v ∈ U. We also give a short and elementary proof of a theorem of Awtar [1] which extends a well known result of Herstein [5] on Lie ideals.