Krull's principal ideal theorem: Difference between revisions
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==Statement== | ==Statement== | ||
Let <math>R</math> be a [[Noetherian ring|Noetherian]] and <math>x \in R</math>. Let <math>P</ | Let <math>R</math> be a [[Noetherian ring|Noetherian]] and <math>x \in R</math>. Let <math>P</math> be a minimal prime ideal among those containing <math>x</math>. Then, the codimension of <math>P</math> is at most 1. | ||
==Generalizations== | ==Generalizations== | ||
* [[Krull's height theorem]]: This is often also called the ''final version'' of the principal ideal theorem. | * [[Krull's height theorem]]: This is often also called the ''final version'' of the principal ideal theorem. | ||
Revision as of 10:00, 7 August 2007
Statement
Let be a Noetherian and . Let be a minimal prime ideal among those containing . Then, the codimension of is at most 1.
Generalizations
- Krull's height theorem: This is often also called the final version of the principal ideal theorem.