##  [Noncatenary Ring](/noncatenary-ring) 

  ##  [Noncatenary Ring](https://algebra.quantumdictionary.io/noncatenary-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 commutative ring in which there exist two prime ideals p ⊂ q for which saturated chains of prime ideals between p and q have different finite lengths; equivalently, the ring fails the catenary property that requires all saturated chains between two primes to have the same length.