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Notes on generalized derivations on Lie ideals in prime rings. (English) Zbl 1176.16030
Let \(L\) be a noncommutative Lie ideal of a prime ring \(R\), let \(H\) be a nonzero generalized derivation of \(R\), and let \(s,t\) be nonnegative integers. The main result states that \(u^sH(u)u^t=0\) for all \(u\in L\) unless \(\text{char}(R)=2\) and \(R\) satisfies the standard identity of degree \(4\).

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