##  [Noncoherent Ring](/index.php/noncoherent-ring) 

  ##  [Noncoherent Ring](https://algebra.quantumdictionary.io/noncoherent-ring-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A ring in which some finitely generated ideal is not finitely presented; equivalently, there exists a homomorphism between finitely generated free modules whose kernel is not finitely generated. This is the failure of coherence.