##  [Buchberger's Criterion](/buchbergers-criterion) 

  ##  [Buchberger's Criterion](https://algebra.quantumdictionary.io/buchbergers-criterion-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 characterization stating that a finite set of polynomials is a Gröbner basis (for a fixed monomial order) if and only if every S-polynomial of every pair of elements of the set reduces to zero modulo that set.