##  [Artinian Algebra](/artinian-algebra) 

  ##  [Artinian Algebra](https://algebra.quantumdictionary.io/artinian-algebra-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An associative algebra that satisfies the descending chain condition on two-sided ideals (equivalently has finite length as a module over itself), often called Artinian when this property holds on both left and right ideals in the associative context.