Rocky Mountain Journal of Mathematics

Jordan [! \large !]$\sigma $-derivations of prime rings

Tsiu-Kwen Lee

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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.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 2 (2017), 511-525.

Dates
First available in Project Euclid: 18 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1492502548

Digital Object Identifier
doi:10.1216/RMJ-2017-47-2-511

Mathematical Reviews number (MathSciNet)
MR3635372

Zentralblatt MATH identifier
1371.16020

Subjects
Primary: 16N60: Prime and semiprime rings [See also 16D60, 16U10] 16R60: Functional identities 16W25: Derivations, actions of Lie algebras

Keywords
Prime ring (Jordan) $\sigma $-derivation PI GPI functional identity

Citation

Lee, Tsiu-Kwen. Jordan [! \large !]$\sigma $-derivations of prime rings. Rocky Mountain J. Math. 47 (2017), no. 2, 511--525. doi:10.1216/RMJ-2017-47-2-511. https://projecteuclid.org/euclid.rmjm/1492502548


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