A note on derivations and Jordan ideals of prime rings

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...

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Main Authors:	Gurninder S. Sandhu, Deepak Kumar
Format:	Article
Language:	English
Published:	AIMS Press 2017-11-01
Series:	AIMS Mathematics
Subjects:	Prime rings\| Jordan ideals\| Generalized derivations\| Martindale ring of quotients\|Generalized polynomial identities (GPIs)
Online Access:	http://www.aimspress.com/article/10.3934/Math.2017.4.580/fulltext.html

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spelling	doaj-85134053fdbf4bc4baefb923137aea6a2020-11-25T00:13:47ZengAIMS PressAIMS Mathematics2473-69882017-11-012458058510.3934/Math.2017.4.580A note on derivations and Jordan ideals of prime ringsGurninder S. Sandhu0Deepak Kumar1Department of Mathematics, Punjabi University, Patiala, Punjab-147001, INDIADepartment of Mathematics, Punjabi University, Patiala, Punjab-147001, INDIALet <em>F</em> : R → R be a generalized derivation of a 2-torsion free prime ring <em>R</em> together witha derivation <em>d</em>: 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 <em>F</em>([x,y]) ∈ Z(R) for all x, y ∈ <em>J</em>; then R is commutative.Consequently, it extends a result of Oukhtite, Mamouni and Ashraf.http://www.aimspress.com/article/10.3934/Math.2017.4.580/fulltext.htmlPrime rings\| Jordan ideals\| Generalized derivations\| Martindale ring of quotients\|Generalized polynomial identities (GPIs)
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Gurninder S. Sandhu Deepak Kumar
spellingShingle	Gurninder S. Sandhu Deepak Kumar A note on derivations and Jordan ideals of prime rings AIMS Mathematics Prime rings\| Jordan ideals\| Generalized derivations\| Martindale ring of quotients\|Generalized polynomial identities (GPIs)
author_facet	Gurninder S. Sandhu Deepak Kumar
author_sort	Gurninder S. Sandhu
title	A note on derivations and Jordan ideals of prime rings
title_short	A note on derivations and Jordan ideals of prime rings
title_full	A note on derivations and Jordan ideals of prime rings
title_fullStr	A note on derivations and Jordan ideals of prime rings
title_full_unstemmed	A note on derivations and Jordan ideals of prime rings
title_sort	note on derivations and jordan ideals of prime rings
publisher	AIMS Press
series	AIMS Mathematics
issn	2473-6988
publishDate	2017-11-01
description	Let <em>F</em> : R → R be a generalized derivation of a 2-torsion free prime ring <em>R</em> together witha derivation <em>d</em>: 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 <em>F</em>([x,y]) ∈ Z(R) for all x, y ∈ <em>J</em>; then R is commutative.Consequently, it extends a result of Oukhtite, Mamouni and Ashraf.
topic	Prime rings\| Jordan ideals\| Generalized derivations\| Martindale ring of quotients\|Generalized polynomial identities (GPIs)
url	http://www.aimspress.com/article/10.3934/Math.2017.4.580/fulltext.html
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A note on derivations and Jordan ideals of prime rings

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