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# Lie Derivations in Prime Rings With Involution

Published:1999-09-01
Printed: Sep 1999
• Gordon A. Swain
• Philip S. Blau
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## 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 - 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