An Engel Type Condition with Vanishing Derivations on Lie Ideals

Let R be a prime ring of characteristic different from 2, Z(R) the center of R, d and δ derivations of R, L a non-central Lie ideal of R. We prove that if δ[[d(u) ,u ] ,d (u)] = 0 for all u ∈ L then either d =0 or δ =0 . Mathematics Subject Classification: 16N60; 16W25