##  [Non-Noetherian](/non-noetherian) 

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

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An algebraic object (ring, module, etc.) is non-Noetherian if it fails the ascending chain condition (ACC) on subobjects or ideals: there exists an infinite strictly increasing chain I1 ⊂ I2 ⊂ I3 ⊂ ··· of subobjects.