Abstract
We prove nilpotency results for Lie algebras over an arbitrary field admitting a derivation, which satisfies a given polynomial identity r(t) = 0. In the special case of the polynomial we obtain a uniform bound on the nilpotency class of Lie algebras admitting a periodic derivation of order n. We even find an optimal bound on the nilpotency class in characteristic p if p does not divide a certain invariant ρn .
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