文摘
Let R be a prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, F and G, the two nonzero generalized derivations of R, I an ideal of R and \(f(x_1,\ldots ,x_n)\) a multilinear polynomial over C which is not central valued on R. If $$\begin{aligned} F(G(f(x_1,\ldots ,x_n))f(x_1,\ldots ,x_n))=0 \end{aligned}$$for all \(x_1,\ldots ,x_n \in I\), then one of the followings holds: (1) there exist \(a,b\in U\) such that \(F(x)=ax\) and \(G(x)=bx\) for all \(x\in R\) with \(ab=0\); (2) there exist \(a,b,p\in U\) such that \(F(x)=ax+xb\) and \(G(x)=px\) for all \(x\in R\) with \(F(p)=0\) and \(f(x_1,\ldots ,x_n)^2\) is central valued on R. We also obtain some related results in cases where R is a semiprime ring and Banach algebra. Keywords Prime ring Derivation Generalized derivation Extended centroid Utumi quotient ring Banach algebra Mathematics Subject Classification 16W25 16N60 Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (25) References1.Argaç, N., De Filippis, V.: Actions of generalized derivations on multilinear polynomials in prime rings. Algebra Colloq. 18(Spec 01), 955–964 (2011)MathSciNetCrossRefMATH2.Argaç, N., Demir, Ç.: Generalized derivations of prime rings on multilinear polynomials with annhilator conditions. Turk. J. Math. 37(2), 231–243 (2013)MATH3.Demir, Ç., Argaç, N.: Prime rings with generalized derivations on right ideals. 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Department of Mathematics, Belda College, Belda, Paschim Medinipur, W.B., 721424, India 2. Department of Mathematics, Science Faculty, Ege University, 35100, Bornova, Izmir, Turkey Continue reading... To view the rest of this content please follow the download PDF link above.