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Journals / Hacettepe Journal of Mathematics and Statistics / 2014 / Cilt: 43 - Sayı: 1

GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT

IDEALS OF PRIME RINGS
Pages
69–83
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

C and f(x1, . . . , xn)2is central valued on R.

📌 3 Key Takeaways

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Objective & Hypothesis:Let R be a prime ring, f (x, . . . , x) a multilinear polynomial over Cin n noncommuting indeterminates, I a nonzero right ideal of R, andF : R-> R be a nonzero generalized skew derivation of R.Suppose that F (f (r, . . . , rn))f (r, . . . , r)?
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Key Findings & Data:C, for all r1, . . . , rn?
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Conclusion & Impact:C and f(x1, . . . , xn)2is central valued on R.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Let R be a prime ring, f (x, . . . , x) a multilinear polynomial over Cin n noncommuting indeterminates, I a nonzero right ideal of R, andF : R-> R be a nonzero generalized skew derivation of R.Suppose that F (f (r, . . . , rn))f (r, . . . , r)? C, for all r1, . . . , rn? I.If f (x1, . . . , xn) is not central valued on R, then either char(R) = 2and R satisfies s4or one of the following holds:(i) f (x1, . . . , xn)xn+1is an identity for I;(ii) F (I)I = (0);(iii) [f (x1, . . . , xn), xn+1]xn+2is an identity for I, there existb, c, q? Q with q an invertible element such that F (x) =bx- qxq-1c for all x? R, and q-1cI? I. Moreover, inthis case either (b- c)I = (0) or b - c ? C and f(x1, . . . , xn)2is central valued on R.

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Cite This Article

RINGS, I. O. P. (2022). GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT. Hacettepe Journal of Mathematics and Statistics, Cilt: 43 - Sayı: 1, 69–83. https://ajindex.com/articles/530360

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