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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