Krull’s principal ideal theorem

Let R be a Noetherian ringMathworldPlanetmath, and P be a prime idealMathworldPlanetmathPlanetmathPlanetmath minimal over a principal idealMathworldPlanetmathPlanetmath (x). Then the height ( of P, that is, the dimension ( of RP, 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