[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c160146

ON JORDAN IDEALS IN PRIME RINGS WITH GENERALIZED DERIVATIONS

Bennis, Driss (Department of Mathematics Faculty of Sciences Mohammed V University in Rabat)
Fahid, Brahim (Department of Mathematics Faculty of Sciences Mohammed V University in Rabat)
Mamouni, Abdellah (Department of Mathematics Faculty of Sciences and Techniques Moulay Ismail University)

Publication Information

Communications of the Korean Mathematical Society / v.32, no.3, 2017 , pp. 495-502 More about this Journal

Abstract

Let R be a 2-torsion free prime ring and J be a nonzero Jordan ideal of R. Let F and G be two generalized derivations with associated derivations f and g, respectively. Our main result in this paper shows that if F(x)x - xG(x) = 0 for all $x{\in}J$ , then R is commutative and F = G or G is a left multiplier and F = G + f. This result with its consequences generalize some recent results due to El-Soufi and Aboubakr in which they assumed that the Jordan ideal J is also a subring of R.

Keywords

prime rings; generalized derivations; Jordan ideals;

Citations & Related Records

Reference

1	R. Awtar, Lie and jordan structure in prime rings with derivations, Proc. Amer. Math. Soc. 41 (1973), 67-74. DOI
2	M. Bresar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), no. 1, 89-93. DOI
3	M. Bresar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), no. 2, 385-394. DOI
4	M. El-Soufi and A. Aboubakr, Generalized derivations on Jordan ideals in prime rings, Turkish J. Math. 38 (2014), no. 2, 233-239. DOI
5	L. Oukhtite and A. Mamouni, Generalized derivations centralizing on Jordan ideals of rings with involution, Turkish J. Math. 38 (2014), no. 2, 225-232. DOI
6	E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100. DOI
7	S. M. A. Zaidi, M. Ashraf, and S. Ali, On Jordan ideals and left ( $\theta;\theta$ )-derivations in prime rings, Int. J. Math. Math. Sci. 2004 (2004), no. 37-40, 1957-1964. DOI