Spectrum is T0: Difference between revisions
(New page: {{spectrum topology fact}} ==Statement== ===Verbal statement=== The spectrum of a commutative unital ring is a T0 space: given any two points, it cannot happen that each one...) |
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Revision as of 21:11, 15 March 2008
This article gives a fact about the relation between ring-theoretic assumptions about a commutative unital ring and topological consequences for the spectrum
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Statement
Verbal statement
The spectrum of a commutative unital ring is a T0 space: given any two points, it cannot happen that each one is in the closure of the other one.
Proof
The proof follows directly from the following fact: given two prime ideals, such that each is contained in the other, the ideals must be equal.