##  [Codimension](/codimension) 

  ##  [Codimension](https://algebra.quantumdictionary.io/codimension-0) 

  

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**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Codimension is a numerical measure comparing an ambient dimension to the dimension of a subobject; for a prime ideal p in a Noetherian ring R, coheight (codimension) is dim(R) - height(p), and for a subvariety it is the difference between ambient and subvariety dimensions.