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On Lie ideals and Jordan left derivations of prime rings. (English) Zbl 1030.16018

Summary: Let \(R\) be a 2-torsion free prime ring and let \(U\) be a Lie ideal of \(R\) such that \(u^2\in U\) for all \(u\in U\). In the present paper it is shown that if \(d\) is an additive mapping of \(R\) into itself satisfying \(d(u^2)=2ud(u)\) for all \(u\in U\), then \(d(uv)=ud(v)+vd(u)\) for all \(u,v\in U\).

MSC:

16W25 Derivations, actions of Lie algebras
16N60 Prime and semiprime associative rings
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
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