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A NOTE ON $(m,n)$-JORDAN DERIVATIONS OF RINGS AND BANACH ALGEBRAS

Part of: Topological (rings and) algebras with an involution Radicals and radical properties of rings

Published online by Cambridge University Press:  28 October 2015

IRENA KOSI-ULBL  and
JOSO VUKMAN
IRENA KOSI-ULBL*
Affiliation:
Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia email irena.kosi@um.si
JOSO VUKMAN
Affiliation:
Department of Mathematics and Computer Science, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia email joso.vukman@guest.um.si
*
✉irena.kosi@um.si
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Abstract

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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.

Keywords

prime ringsemiprime ringBanach algebraderivationJordan derivationleft derivationleft Jordan derivation(m, n)-Jordan derivation

MSC classification

Primary: 16N60: Prime and semiprime rings
Secondary: 46K15: Hilbert algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 2 , April 2016 , pp. 231 - 237
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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