A note on derivations and Jordan ideals of prime rings

Gurninder S. Sandhu; Deepak Kumar

doi:10.3934/Math.2017.4.580

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

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A note on derivations and Jordan ideals of prime rings

Gurninder S. Sandhu, Deepak Kumar

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

Received: , Accepted: , Published:

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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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This article has been cited by:

1. Gurninder S. Sandhu, Deepak Kumar, Correction: A note on derivations and Jordan ideals in prime rings, AIMS Mathematics, 2019, 4, 3, 684, 10.3934/math.2019.3.684
2. Abdulrahman H. Majeed, Shahed Ali Hamil, Derivations in Gamma Rings with γ-Lie and γ-Jordan Structures, Journal of Physics: Conference Series, 2020, 1530, 012049, 10.1088/1742-6596/1530/1/012049

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Copyright Info: 2017, Gurninder S. Sandhu, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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