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

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

  

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**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The situation that there exist finitely generated modules which are not injective; finite generation does not force injectivity, so such modules fail extension-lifting properties that characterize injective objects.