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 $n$.