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2017 Jordan [! \large !]$\sigma $-derivations of prime rings
Tsiu-Kwen Lee
Rocky Mountain J. Math. 47(2): 511-525 (2017). DOI: 10.1216/RMJ-2017-47-2-511

Abstract

Let $R$ be a noncommutative prime ring with extended centroid~$C$ and with $Q_{mr}(R)$ its maximal right ring of quotients. From the viewpoint of functional identities, we give a complete characterization of Jordan $\sigma $-derivations of $R$ with $\sigma $ an epimorphism. Precisely, given such a Jordan $\sigma $-derivation $\de \colon R\to Q_{mr}(R)$, it is proved that either $\delta $ is a $\sigma $-derivation or a derivation $d\colon R\to Q_{mr}(R)$ and a unit $u\in Q_{mr}(R)$ exist such that $\delta (x)=ud(x)+\mu (x)u$ for all $x\in R$, where $\mu \colon R\to C$ is an additive map satisfying $\mu (x^2)=0$ for all $x\in R$. In addition, if $\sigma $ is an X-outer automorphism, then $\delta $ is always a $\sigma $-derivation.

Citation

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Tsiu-Kwen Lee. "Jordan [! \large !]$\sigma $-derivations of prime rings." Rocky Mountain J. Math. 47 (2) 511 - 525, 2017. https://doi.org/10.1216/RMJ-2017-47-2-511

Information

Published: 2017
First available in Project Euclid: 18 April 2017

zbMATH: 1371.16020
MathSciNet: MR3635372
Digital Object Identifier: 10.1216/RMJ-2017-47-2-511

Subjects:
Primary: 16N60, 16R60, 16W25

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 2 • 2017
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