---
type: "concept"
title: "Hilbert's weak Nullstellensatz"
slug: "hilberts-weak-nullstellensatz"
language: "en"
translationGroupId: "cmrbtyd660007ls01avbxulo5"
domain: "Algebra"
status: "stub"
aliases: []
lastEditedBy: "ancient-tree"
---

If $k$ is an [[Algebraically closed field|algebraically closed field]], then every [[Maximal ideal|maximal ideal]] of the [[Polynomial ring|ring of polynomials]] $k[x_{1},\ldots,x_{n}]$ is an [[Ideal generated by polynomials|ideal generated by polynomials]], of the form $(x_{1}-a_{1},\ldots,x_{n}-a_{n})$ for some point $(a_{1},\ldots,a_{n})$ in the [[Affine space over a field|affine space]] $\mathbb{A}^{n}_{k}$.