##  [Krull's Principal Ideal Theorem](/krulls-principal-ideal-theorem) 

  ##  [Krull's Principal Ideal Theorem](https://algebra.quantumdictionary.io/krulls-principal-ideal-theorem-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A theorem in dimension theory which states that in a Noetherian ring R, any minimal prime ideal lying over a principal ideal (f) has height at most one; equivalently, the height of any minimal prime over an ideal generated by r elements is at most r (in particular the principal ideal case gives bound one).