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Krull's principal ideal theorem (Theorem)

Let $ R$ be a Noetherian ring, and $ P$ be a prime ideal minimal over a principal ideal $ (x)$. Then the height of $ P$, that is, the dimension 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$.



"Krull's principal ideal theorem" is owned by drini. [ full author list (2) | owner history (2) ]
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Cross-references: ideal generated by, minimal prime, principal ideal, minimal, prime ideal, noetherian ring
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This is version 2 of Krull's principal ideal theorem, born on 2002-12-05, modified 2004-04-22.
Object id is 3664, canonical name is KrullsPrincipalIdealTheorem.
Accessed 2168 times total.

Classification:
AMS MSC: 13C15 (Commutative rings and algebras :: Theory of modules and ideals :: Dimension theory, depth, related rings )
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