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A Combinatorial Proof of the Effective Nullstellensatz

✍ Scribed by Thomas W. Dubé

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
481 KB
Volume
15
Category
Article
ISSN
0747-7171

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✦ Synopsis

Let (I) be an ideal in the affine multi-variate polynomial ring (\mathcal{A}=K\left[x_{1}, \ldots, x_{n}\right]). Beginning with the work of Brownawell, there has been renewed interest in recent years in using the degrees of polynomials which generate (I) to bound the degree (D) such that:

[
g \in \sqrt{I} \Rightarrow g^{D} \in I
]

This paper will prove the degree bound (D) using only counting arguments for the ideal 1. This provides the first combinatorial proof of the effective Nullstellensatz.

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