An Identity with Skew Derivations on Lie Ideals

Abstract

Let $R$ be a 2-torsion free prime ring and $L$ a noncommutative Lie ideal of $R$. Suppose that $(d, σ)$ is a skew derivation of $R$ such that $x^s d(x)x^t = 0$ for all $x ∈ L$, where $s, t$ are fixed non-negative integers. Then $d = 0$.