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Commutator identity involving generalized derivations on multilinear polynomials
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Let R be a prime ring of characteristic different from 2 with Utumi quotient ring U, C be the extended centroid of \(R,\, F\) and G be two nonzero generalized derivations of R and \(f(x_1,\ldots ,x_n)\) be a multilinear polynomial over C which is not central valued on R. If $$\begin{aligned} {[}F(u)u, G(v)v]=0 \end{aligned}$$for all \(u,v\in f(R)\), then there exist \(a,b\in U\) such that \(F(x)=ax\) and \(G(x)=bx\) for all \(x\in R\) with \([a, b]=0\) and \(f(x_1,\ldots ,x_n)^2\) is central valued on R.KeywordsPrime ringGeneralized derivationMultilinear polynomialMathematics Subject Classification16W2516N60References1.Ali, A., De Filippis, V., Shujat, F.: Commuting values of generalized derivations on multilinear polynomials. Commun. Algebra 42(9), 3699–3707 (2014)MathSciNetCrossRefMATHGoogle Scholar2.Argaç, N., Demir, Ç.: Prime rings with generalized derivations on right ideals. 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Soc. 8, 1093–1100 (1957)MathSciNetCrossRefMATHGoogle ScholarCopyright information© Università degli Studi di Ferrara 2016Authors and AffiliationsBasudeb Dhara1Mohd Arif Raza2Email authorNadeem Ur Rehman31.Department of MathematicsBelda CollegePaschim MedinipurIndia2.Department of MathematicsAligarh Muslim UniversityAligarhIndia3.Department of Mathematics, Faculty of scinceTaibah UniversityAl-MadinahSaudi Arabia About this article CrossMark Print ISSN 0430-3202 Online ISSN 1827-1510 Publisher Name Springer Milan About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s11565-016-0255-x_Commutator identity involving gene", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s11565-016-0255-x_Commutator identity involving gene", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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