Elimination ideals and Bezout relations

2019/06/01 by Galigo, Andre, Jelonek, Zbigniew
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.00231

Abstract

Let k be an infinite field and I⊂ k [x₁, … ,x_n] be an ideal such that dim V(I)=q. Denote by (f₁, …, f_s) a set of generators of I. One can see that in the set I∩ k [x₁,...,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 Bézout (i.e. membership) relation expressing such a polynomial as a combination of the f_i.

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