Geodesic
On Jordan ideals and derivations in rings with involution
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 3, pp. 389-395 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 16N16, 16U70, 16U80, 16W10, 16W25
Keywords: $\ast$-prime rings; Jordan ideals; derivations 
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     author = {Oukhtite, Lahcen},
     title = {On {Jordan} ideals and derivations in rings with involution},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {389--395},
     year = {2010},
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     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_2010_51_3_a0/}
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Oukhtite, Lahcen. On Jordan ideals and derivations in rings with involution. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 3, pp. 389-395. http://geodesic.mathdoc.fr/item/CMUC_2010_51_3_a0/