##  [Descending Chain Condition](/descending-chain-condition) 

  ##  [Descending Chain Condition](https://puremath.quantumdictionary.io/descending-chain-condition-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A condition on an ordered set or class of subobjects that every descending chain eventually stabilizes: there exists N such that for all n≥N the nth member equals the Nth member. Equivalently, there are no infinite strictly decreasing sequences. Commonly applied to ideals, modules, and other substructures.