Commutative algebra Dimension theory Concept
Height of a prime ideal
Summary
The height of a prime ideal is the largest length of a strictly increasing chain of prime ideals that ends at . It equals the Krull dimension of the localization at , and it is the algebraic notion of codimension. Krull's principal ideal theorem and Krull's height theorem bound the height by the number of generators of an ideal.
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| Tag | 87WH65FJB8 |
|---|---|
| URI | m2://87WH65FJB8 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 13C15 |
| Changed | 2 November 2026 |
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Definitions
Used by
- Determinantal ideal
- Serre's criterion for normality
- Divisor class group
- Nagata's example of a Noetherian ring of infinite dimension