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Journals / Karaelmas Fen ve Mühendislik Dergisi / 2017 / Cilt: 7 - Sayı: 2

Explicit Gröbner Basis of the Ideal of Vanishing Polynomials over Z2 ×Z2

Z2 ×Z2 Üzerinde Sıfırlanan Polinomların İdealinin Açık Gröbner Tabanı

Abdullah ÇAĞMAN
Pages
349–351
Publication Date
2022-10-19
DOI
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AI Summary & Key Takeaways

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

Our proof is based fully on a combinatorial way

📌 3 Key Takeaways

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Objective & Hypothesis:Vanishing polynomials form an ideal of polynomial ring over the coefficient ring.
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Key Findings & Data:In this paper, we give some vanishing polynomialsof the polynomial ring Z Z m l # 6x x 1 2 , , ..., x n@ where (m,l)≠1 and an explicit minimal strong Gröbner basis of the ideal of vanishingpolynomials of the ring Z Z 2 2 # [x].
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Conclusion & Impact:Our proof is based fully on a combinatorial way
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Vanishing polynomials form an ideal of polynomial ring over the coefficient ring. In this paper, we give some vanishing polynomialsof the polynomial ring Z Z m l # 6x x 1 2 , , ..., x n@ where (m,l)≠1 and an explicit minimal strong Gröbner basis of the ideal of vanishingpolynomials of the ring Z Z 2 2 # [x]. Our proof is based fully on a combinatorial way

Özet

Sıfırlanan polinomlar, katsayı halkası üzerinde tanımlanan polinom halkalarının bir idealini oluştururlar. Bu makalede (m,l)≠1 olmak üzere Z Z m l # 6x x 1 2 , , ..., x n@ polinom halkasının bazı sıfırlanan polinomlarını ve Z Z 2 2 # [x] halkasının sıfırlanan polinomlarının idealinin açık minimal güçlü Gröbner tabanını vereceğiz. İspatımız tamamen kobinasyonel yönteme dayalı olacaktır.

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Cite This Article

ÇAĞMAN, A. (2022). Explicit Gröbner Basis of the Ideal of Vanishing Polynomials over Z2 ×Z2. Karaelmas Fen ve Mühendislik Dergisi, Cilt: 7 - Sayı: 2, 349–351. https://ajindex.com/articles/570889

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