CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Lie Derivations in Prime Rings With Involution

  Published:1999-09-01
 Printed: Sep 1999
  • Gordon A. Swain
  • Philip S. Blau
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

Let $R$ be a non-GPI prime ring with involution and characteristic $\neq 2,3$. Let $K$ denote the skew elements of $R$, and $C$ denote the extended centroid of $R$. Let $\delta$ be a Lie derivation of $K$ into itself. Then $\delta=\rho+\epsilon$ where $\epsilon$ is an additive map into the skew elements of the extended centroid of $R$ which is zero on $[K,K]$, and $\rho$ can be extended to an ordinary derivation of $\langle K\rangle$ into $RC$, the central closure.
MSC Classifications: 16W10, 16N60, 16W25 show english descriptions Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]
Prime and semiprime rings [See also 16D60, 16U10]
Derivations, actions of Lie algebras
16W10 - Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]
16N60 - Prime and semiprime rings [See also 16D60, 16U10]
16W25 - Derivations, actions of Lie algebras
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/