AIMS Mathematics, 2017, 2(4): 580-585. doi: 10.3934/Math.2017.4.580.

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A note on derivations and Jordan ideals of prime rings

Department of Mathematics, Punjabi University, Patiala, Punjab-147001, INDIA

Let F : R → R be a generalized derivation of a 2-torsion free prime ring R together witha derivation d: In this paper, we show that a nonzero Jordan ideal J of R contains a nonzero ideal ofR. Further, we use this result to prove that if F([x,y]) ∈ Z(R) for all x, y ∈ J; then R is commutative.Consequently, it extends a result of Oukhtite, Mamouni and Ashraf.
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Keywords Prime rings; Jordan ideals; Generalized derivations; Martindale ring of quotients; Generalized polynomial identities (GPIs)

Citation: Gurninder S. Sandhu, Deepak Kumar. A note on derivations and Jordan ideals of prime rings. AIMS Mathematics, 2017, 2(4): 580-585. doi: 10.3934/Math.2017.4.580

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