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A note on Jordan*-derivations in semiprime rings with involution. (English) Zbl 1143.16037

Summary: We prove the following result. Let \(R\) be a 6-torsion free semiprime *-ring and let \(D\colon R\to R\) be an additive mapping satisfying the relation \(D(xyx)=D(x)y^*x^*+xD(y)x^*+xyD(x)\), for all pairs \(x,y\in R\). In this case \(D\) is a Jordan *-derivation.

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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