Previous |  Up |  Next


$\ast$-prime rings; Jordan ideals; derivations
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.
[1] Ashraf M., Ali A., Rehman N.: On Lie ideals with derivations as homomorphisms and anti-homomorphisms. Acta Math. Hungar. 101 (2003), 79–82. DOI 10.1023/B:AMHU.0000003893.61349.98 | MR 2011464
[2] Bell H.E., Kappe L.C.: Rings in which derivations satisfy certain algebraic conditions. Acta Math. Hungar. 53 (1989), 339–346. DOI 10.1007/BF01953371 | MR 1014917 | Zbl 0705.16021
[3] Oukhtite L., Salhi S., Taoufiq L.: $\sigma$-Lie ideals with derivations as homomorphisms and anti-homomorphisms. Int. J. Algebra 1 (2007), no. 5, 235–239. MR 2342996 | Zbl 1124.16028
[4] Oukhtite L., Salhi S.: On generalized derivations of $\sigma $-prime rings. Afr. Diaspora J. Math. 5 (2007), no. 1, 21–25. MR 2337187
[5] Zaidi S.M.A., Ashraf M., Ali S.: On Jordan ideals and left $(\theta ,\theta)$-derivations in prime rings. Int. J. Math. Math. Sci. 2004 (2004), no. 37–40, 1957–1964. DOI 10.1155/S0161171204309075 | MR 2100888 | Zbl 1069.16041
[6] Posner E.C.: Derivations in prime rings. Proc. Amer. Math. Soc. 8 (1957), 1093–1100. DOI 10.1090/S0002-9939-1957-0095863-0 | MR 0095863 | Zbl 0082.03003
Partner of
EuDML logo