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

Abdullah ÇAĞMAN

Abstract


Vanishing polynomials form an ideal of polynomial ring over the coefficient ring. In this paper, we give some vanishing polynomials of the polynomial ring Zm×Zl[x1,x2,…,xn] where (m,l)≠1 and an explicit minimal strong Gröbner basis of the ideal of vanishing polynomials of the ring Z2×Z2[x]. Our proof is based fully on a combinatorial way.

Keywords


Vanishing polynomial, Polynomial ring, Vanishing Ideal, Gröbner Basis

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DOI: http://dx.doi.org/10.7212%2Fzkufbd.v7i2.797

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