 ##  [Height of a Prime Ideal](/height-prime-ideal) 

  ##  [Height of a Prime Ideal](https://puremath.quantumdictionary.io/height-prime-ideal-0) 

  
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- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

The supremum of lengths n of strictly increasing chains of prime ideals p0 ⊊ p1 ⊊ ... ⊊ pn that terminate at the given prime ideal p; equivalently the Krull codimension of p inside the spectrum, providing a local measure of dimension.