Krull’s principal ideal theorem

Let $R$ be a Noetherian ring, and $P$ be a prime ideal minimal over a principal ideal $(x)$. Then the height (http://planetmath.org/HeightOfAPrimeIdeal) of $P$, that is, the dimension (http://planetmath.org/KrullDimension) of $R_P$, is less than 1. More generally, if $P$ is a minimal prime of an ideal generated by $n$ elements, the height of $P$ is less than $n$.

Title	Krull’s principal ideal theorem
Canonical name	KrullsPrincipalIdealTheorem
Date of creation	2013-03-22 13:12:08
Last modified on	2013-03-22 13:12:08
Owner	drini (3)
Last modified by	drini (3)
Numerical id	5
Author	drini (3)
Entry type	Theorem
Classification	msc 13C15