##  [Ascending Chain Condition](/ascending-chain-condition) 

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

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A property of a partially ordered set or a class of subobjects stating that every ascending chain stabilizes: there exists N such that for all n≥N the nth member equals the (N)th member. Equivalently, there is no infinite strictly increasing sequence. Often used for ideals, submodules, or subobjects.