Krull dimension

If $R$ is a ring, the Krull dimension (or simply dimension) of $R$ , $\dim R$ is the supremum of all integers $n$ such that there is an increasing sequence of prime ideals $\mathfrak{p}_{0}\subsetneq\cdots\subsetneq\mathfrak{p}_{n}$ of length $n$ in $R$ .

If $X$ is a topological space, the Krull dimension (or simply dimension) of $X$ , $\dim X$ is the supremum of all integers $n$ such that there is a decreasing sequence of irreducible closed subsets $F_{0}\supsetneq\cdots\supsetneq F_{n}$ 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