##  [Non-Noetherian Ring](/index.php/non-noetherian-ring) 

  ##  [Non-Noetherian Ring](https://algebra.quantumdictionary.io/non-noetherian-ring-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A ring (usually commutative with unity in this context) that does not satisfy the ascending chain condition on ideals: there exists an infinite strictly ascending chain of ideals, and ideals need not be finitely generated.