On generalized Jordan *-derivation in rings. (English) Zbl 1295.16032
Summary: Let \(n\geqslant 1\) be a fixed integer and let \(R\) be an \((n+1)!\)-torsion free *-ring with identity element \(e\). If \(F,d\colon R\to R\) are two additive mappings satisfying \(F(x^{n+1})=F(x)(x^*)^n+xd(x)(x^*)^{n-1}+x^2d(x)(x^*)^{n-2}+\cdots+x^nd(x)\) for all \(x\in R\), then \(d\) is a Jordan *-derivation and \(F\) is a generalized Jordan *-derivation on \(R\).
MSC:
| 16W25 | Derivations, actions of Lie algebras |
| 16W10 | Rings with involution; Lie, Jordan and other nonassociative structures |
| 16N60 | Prime and semiprime associative rings |
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