Abstract
Let R be a prime ring and set [x, y]1 = [x, y] = xy − yx for $${x,y\in R}$$ and inductively [x, y] k = [[x, y]k-1, y] for k > 1. We apply the theory of generalized polynomial identities with automorphisms and skew derivations to obtain the following result: If δ is a nonzero σ-derivation of R and L is a noncommutative Lie ideal of R so that [δ(x), x] k = 0 for all $${x \in L}$$ , where k is a fixed positive integer, then charR = 2 and $${R\subseteq M_{2}(F)}$$ for some field F. This result generalizes the case of derivations by Lanski and also the case of automorphisms by Mayne.
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