Abstract
Let R be a prime ring with characteristic different from 2 and 3, $$Q_r$$ be its right Martindale quotient ring, C be its extended centroid, F a nonzero generalized skew derivation of R and L a noncentral Lie ideal of R. If $$\begin{aligned}{}[[F(u),u],F(u)]\in Z(R) \end{aligned}$$for all $$u\in L$$, then one of the following holds:
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