Krull dimension

If R is a ring, the Krull dimensionMathworldPlanetmath (or simply dimensionMathworldPlanetmathPlanetmath) of R, dimR is the supremumPlanetmathPlanetmath of all integers n such that there is an increasing sequence of prime idealsMathworldPlanetmathPlanetmathPlanetmath 𝔭0𝔭n of length n in R.

If X is a topological spaceMathworldPlanetmath, the Krull dimension (or simply dimension) of X, dimX is the supremum of all integers n such that there is a decreasing sequence of irreduciblePlanetmathPlanetmathPlanetmath closed subsets F0Fn of X.

Title Krull dimension
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