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AIMS Mathematics

2017, Volume 2, Issue 4: 580-585. doi: 10.3934/Math.2017.4.580
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Research article

A note on derivations and Jordan ideals of prime rings

  • Department of Mathematics, Punjabi University, Patiala, Punjab-147001, India
  • Received: 14 September 2017 Accepted: 23 October 2017 Published: 01 November 2017

  • MSC : 16W25, 16N60, 16U80

  • Let $F:R\rightarrow R$ be a generalized derivation of a 2-torsion free prime ring $R$ together with a derivation $d.$ In this paper, we show that a nonzero Jordan ideal $J$ of $R$ contains a nonzero ideal of $R$. Further, we use this result to prove that if $F([x, y])\in Z(R)$ for all $x, y\in J, $ then $R$ is commutative. Consequently, it extends a result of Oukhtite, Mamouni and Ashraf.

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

    Related Papers:

  • Let $F:R\rightarrow R$ be a generalized derivation of a 2-torsion free prime ring $R$ together with a derivation $d.$ In this paper, we show that a nonzero Jordan ideal $J$ of $R$ contains a nonzero ideal of $R$. Further, we use this result to prove that if $F([x, y])\in Z(R)$ for all $x, y\in J, $ then $R$ is commutative. Consequently, it extends a result of Oukhtite, Mamouni and Ashraf.


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    [12] K. I. Beidar, W. S. Martindale Ⅲ, A. V. Mikhalev, Rings with Generalized Identities. Pure and Applied Mathematics. vol. 196, Marcel Dekker, New York, 1996.
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  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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