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On Lie ideals and \((\sigma,\tau)\)-Jordan derivations on prime rings. (English) Zbl 1006.16044
Summary: Let \(R\) be a prime ring with characteristic different from two and let \(U\) be a Lie ideal of \(R\) such that \(u^2\in U\) for all \(u\in U\). Suppose that \(\sigma\), \(\tau\) are automorphisms of \(R\). In the present paper, it is shown that if \(d\) is an additive mapping of \(R\) into itself satisfying \(d(u^2)=d(u)\sigma(v)+\tau(u)d(v)\) for all \(u,v\in U\), then \(d(uv)=d(u)\sigma(v)+\tau(u)d(v)\) 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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