##  [Failure of Finite Generation](/index.php/failure-finite-generation) 

  ##  [Failure of Finite Generation](https://algebra.quantumdictionary.io/failure-finite-generation-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/index.php/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The property that an algebraic object (ring, module, algebra, invariant ring, etc.) cannot be generated by finitely many elements, so it is not finitely generated and often not Noetherian.