##  [Hilbert's Nullstellensatz](/hilberts-nullstellensatz) 

  ##  [Hilbert's Nullstellensatz](https://algebra.quantumdictionary.io/hilberts-nullstellensatz-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A collection of related theorems linking ideals in polynomial rings over an algebraically closed field k to algebraic sets in affine space: classically, the (strong) Nullstellensatz states that for an ideal I ⊂ k[x1,…,xn], the ideal of functions vanishing on the zero set V(I) equals the radical rad(I); the weak form identifies maximal ideals with k-rational points.