# 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 KrullsPrincipalIdealTheorem 2013-03-22 13:12:08 2013-03-22 13:12:08 drini (3) drini (3) 5 drini (3) Theorem msc 13C15