Elimination ideals and Bezout relations

JOURNAL OF ALGEBRA

卷:562

Article

Galligo, Andre¹  Jelonek, Zbigniew² 

[1] Univ Cote dAzur, INRIA, LJAD, Nice, France

[2] Polish Acad Sci, Inst Matematyczny, Sniadeckich 8, PL-00656 Warsaw, Poland

关键词: Nullstellensatz;    Polynomials;    Elimination;    Affine variety;   

DOI  :  10.1016/j.jalgebra.2020.06.022

来源: Elsevier

【 摘 要 】

Let k be an infinite field and I subset of k[x(1), ..., x(n)] be a non-zero ideal such that dim V(I) = q >= 0. Denote by (f(1), ..., f(s)) a set of generators of I. One can see that in the set I boolean AND k[x(1), ..., x(q+1)] there exist non-zero polynomials, depending only on these q + 1 variables. We aim to bound the minimal degree of the polynomials of this type, and of a Bezout (i.e. membership) relation expressing such a polynomial as a combination of the f(i). In particular we show that if deg f(i) = d(i) where d(1) >= d(2)... >= d(s), then there exist a non-zero polynomial phi(x) is an element of k[x(1), ..., x(q+1)] boolean AND I, such that deg phi <= d(s) Pi(n-q-1)(i=1) d(i). We also give a relative version of this theorem. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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