##  [Existence of Nonprojective Finitely Generated Module](/existence-nonprojective-finitely-generated-module) 

  ##  [Existence of Nonprojective Finitely Generated Module](https://algebra.quantumdictionary.io/existence-nonprojective-finitely-generated-module-0) 

  

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

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The situation that there exist modules which are finitely generated but not projective; finite generation alone does not guarantee projectivity, so finitely generated modules may lack lifting or splitting properties characteristic of projective modules.