##  [Coherent Ring](/coherent-ring) 

  ##  [Coherent Ring](https://algebra.quantumdictionary.io/coherent-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 ring in which every finitely generated ideal is finitely presented; equivalently, the kernel of any homomorphism between finitely generated free modules is finitely generated. This gives a controlled finiteness of relations among generators.