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Keywords:
$\ast$-prime rings; Jordan ideals; derivations
$\ast$-prime rings; Jordan ideals; derivations
Summary:
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.
References:
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