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.


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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