##  [Cohen–Macaulay Property](/cohen-macaulay-property) 

  ##  [Cohen–Macaulay Property](https://algebra.quantumdictionary.io/cohen-macaulay-property-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 property of a Noetherian local ring or a module meaning that its depth equals its Krull dimension (locally), i.e., it attains maximal possible depth relative to its dimension.