Commutators with idempotent values on multilinear polynomials in prime rings

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• 作者：VINCENZO DE FILIPPIS ; MOHD ARIF RAZA…
• 关键词：Multilinear polynomial ; derivations ; generalized polynomial identity ; prime ring ; right ideal.
• 刊名：Proceedings - Mathematical Sciences
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：127
• 期：1
• 页码：91-98
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer India
• ISSN：0973-7685
• 卷排序：127

文摘

Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R, f(x₁, . . . , x_n) a multilinear polynomial over C, ρ a nonzero right ideal of R and m > 1 a fixed integer such that$$\qquad \left ([d(f(r_{1},\ldots ,r_{n})),f(r_{1},\ldots ,r_{n})]\right )^{m}=[d(f(r_{1},\ldots ,r_{n})),f(r_{1},\ldots ,r_{n})] $$ for all r₁, . . . , r_n∈class="EmphasisTypeItalic ">ρ. Then either [f(x₁,…,x_n),x_n+1]x_n+2 is an identity for ρ or d(ρ)ρ = 0.KeywordsMultilinear polynomialderivationsgeneralized polynomial identityprime ringright ideal.2010 Mathematics Subject Classification.16N6016R5016U8016W25.References[1]Beidar K I, Rings with generalized identities, Moscow Univ. Math. Bull. 33 (1978) 53–58MATHGoogle Scholar[2]Bell H E and Martindale W S III, Centralizing mappings of semiprime rings, Canad. Math. 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