##  [Noether Normalization Lemma](/noether-normalization-lemma) 

  ##  [Noether Normalization Lemma](https://algebra.quantumdictionary.io/noether-normalization-lemma-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 lemma stating that any finitely generated algebra A of finite type over a field k admits a finite injective k-algebra map from a polynomial subring k[y1,…,yd] where d = trdeg_k(Frac(A)); equivalently, after a generic linear change of coordinates A is integral and finite over a polynomial subring in d variables.