Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2016.07.07
  • Accepted : 2016.10.07
  • Published : 2017.07.31
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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.

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References

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