Annihilators of power values of generalized skew derivations on Lie ideals in prime rings

Abstract

Let R be a prime ring of characteristic different from 2, \(n\ge 1\) a fixed integer, C the extended centroid of R, F a generalized skew derivation of R and L a Lie ideal of R. If there exists \(0 \ne a \in R\) such that \(a(F(xy)-yx)^{n}=0\) for all \(x,y\in L\), then L is central, unless R satisfies the standard polynomial identity \(s_4(x_1, \ldots , x_4)\).