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A NOTE ON $(m,n)$-JORDAN DERIVATIONS OF RINGS AND BANACH ALGEBRAS
Part of
- Radicals and radical properties of rings
- Topological (rings and) algebras with an involution
IRENA KOSI-ULBL, JOSO VUKMAN
Journal:

Bulletin of the Australian Mathematical Society / Volume 93 / Issue 2 / April 2016

Published online by Cambridge University Press:

28 October 2015, pp. 231-237

Print publication:

April 2016
- Article
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In this paper we prove the following result: let $m,n\geq 1$ be distinct integers, let $R$ be an $mn(m+n)|m-n|$-torsion free semiprime ring and let $D:R\rightarrow R$ be an $(m,n)$-Jordan derivation, that is an additive mapping satisfying the relation $(m+n)D(x^{2})=2mD(x)x+2nxD(x)$ for $x\in R$. Then $D$ is a derivation which maps $R$ into its centre.