##  [Projective Dimension](/projective-dimension) 

  ##  [Projective Dimension](https://algebra.quantumdictionary.io/projective-dimension-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The minimal length n of a projective resolution ... → P_n → ... → P_0 → M → 0 of a module M in an abelian category with enough projectives; it measures how far M is from being projective (projective dimension 0) by counting required projective steps.