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On Jordan ideals and derivations in rings with involution

Lahcen Oukhtite — 2010

Commentationes Mathematicae Universitatis Carolinae

Let $R$ be a $2$ -torsion free $*$ -prime ring, $d$ a derivation which commutes with $*$ and $J$ a $*$ -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 $*$ -primeness hypothesis is not superfluous.

Jordan ideals and derivations in prime near-rings

Abdelkarim Boua; Lahcen Oukhtite; Abderrahmane Raji — 2014

Commentationes Mathematicae Universitatis Carolinae

In this paper we investigate $3$ -prime near-rings with derivations satisfying certain differential identities on Jordan ideals, and we provide examples to show that the assumed restrictions cannot be relaxed.

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