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Derivations with power central values on Lie ideals in prime rings. (English) Zbl 1165.16303
Summary: Let $$R$$ be a prime ring of $$\text{char\,}R\neq 2$$ with a nonzero derivation $$d$$ and let $$U$$ be its noncentral Lie ideal. If for some fixed integers $$n_1\geq 0$$, $$n_2\geq 0$$, $$n_3\geq 0$$, $$(u^{n_1}[d(u),u]u^{n_2})^{n_3}\in Z(R)$$ for all $$u\in U$$, then $$R$$ satisfies $$S_4$$, the standard identity in four variables.

##### MSC:
 16W25 Derivations, actions of Lie algebras 16N60 Prime and semiprime associative rings 16W10 Rings with involution; Lie, Jordan and other nonassociative structures 16R50 Other kinds of identities (generalized polynomial, rational, involution)
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