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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
##### Keywords:
generalized derivations; prime rings; Lie ideals
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