Krull dimension
If is a ring, the Krull dimension (or simply dimension) of , is the supremum of all integers such that there is an increasing sequence of prime ideals of length in .
If is a topological space, the Krull dimension (or simply dimension) of , is the supremum of all integers such that there is a decreasing sequence of irreducible closed subsets of .
Title | Krull dimension |
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Canonical name | KrullDimension |
Date of creation | 2013-03-22 12:03:27 |
Last modified on | 2013-03-22 12:03:27 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 8 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 54-00 |
Synonym | dimension (Krull) |
Related topic | HeightOfAPrimeIdeal |
Related topic | Dimension3 |