Lahcen Oukhtite
On Jordan ideals and derivations in rings with involution

Comment.Math.Univ.Carolin. 51,3 (2010) 389-395.

Abstract:Let $R$ be a $2$-torsion free $\ast$-prime ring, $d$ a derivation which commutes with $\ast$ and $J$ a $\ast$-Jordan ideal and a subring of $R$. In this paper, it is shown that if either $d$ acts as a homomorphism or as an anti-homomorphism on $J$, then $d=0$ or $J\subseteq Z(R)$. Furthermore, an example is given to demonstrate that the $\ast$-primeness hypothesis is not superfluous.

Keywords: $\ast$-prime rings, Jordan ideals, derivations
AMS Subject Classification: 16W10 16W25 16U80