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

Vanishing polynomials form an ideal of polynomial ring over the coefficient ring. In this paper, we give some vanishing polynomials of 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 vanishing polynomials of the ring Z Z 2 2 # [x]. Our proof is based fully on a combinatorial way

Z2 ×Z2 Üzerinde Sıfırlanan Polinomların İdealinin Açık Gröbner Tabanı

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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