Lie Derivations in Prime Rings With Involution

http://dx.doi.org/10.4153/CMB-1999-047-6
Canad. Math. Bull. 42(1999), 401-411

  Published:1999-09-01
 Printed: Sep 1999

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.