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Krull dimension∗
mathcam†
2013-03-21 12:58:12
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 p0 ( · · · ( pn 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 F0 ) · · · ) Fn of X.
∗ hKrullDimensioni created: h2013-03-21i by: hmathcami version: h31107i Privacy
setting: h1i hDefinitioni h54-00i
† This text is available under the Creative Commons Attribution/Share-Alike License 3.0.
You can reuse this document or portions thereof only if you do so under terms that are
compatible with the CC-BY-SA license.
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