##  [Non-Artinian](/non-artinian) 

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

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An algebraic object (ring, module, etc.) is non-Artinian if it fails the descending chain condition (DCC): there exists an infinite strictly decreasing chain I1 ⊃ I2 ⊃ I3 ⊃ ··· of subobjects that does not stabilize.