##  [Regular Local Ring](/regular-local-ring) 

  ##  [Regular Local Ring](https://algebra.quantumdictionary.io/regular-local-ring-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 Noetherian local ring (R, m) whose Krull dimension equals the minimal number of generators of its maximal ideal m; equivalently R has finite global (homological) dimension equal to that Krull dimension.