A note on derivations and Jordan ideals of prime rings

A note on derivations and Jordan ideals of prime rings

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...

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Bibliographic Details
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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Summary:	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.
ISSN:	2473-6988