Krull's principal ideal theorem: Difference between revisions

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Let $R$ be a Noetherian and $x \in R$ . Let $P$ be a minimal prime ideal among those containing $x$ . Then, the codimension of $P$ is at most 1.

Krull's height theorem: This is often also called the final version of the principal ideal theorem.
Determinantal ideal theorem: This generalizes the principal ideal theorem to the ideal generated by the determinants of minors of a matrix

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	* [[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.
			* [[Determinantal ideal theorem]]: This generalizes the principal ideal theorem to the ideal generated by the determinants of minors of a matrix