“Constructible topology”的意思、由来-开放百科全书

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Constructible topology

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In commutative algebra, the constructible topology on the spectrum of a commutative ring is a topology where each closed set is the image of in for some algebra B over A. An important feature of this construction is that the map is a closed map with respect to the constructible topology.

With respect to this topology, is a compact,^[1] Hausdorff, and totally disconnected topological space. In general the constructible topology is a finer topology than the Zariski topology, but the two topologies will coincide if and only if is a von Neumann regular ring, where is the nilradical of A.

Despite the terminology being similar, the constructible topology is not the same as the set of all constructible sets.^[2]

References

1. ^Some authors prefer the term quasicompact here.
2. ^{{Cite web|url=http://math.stackexchange.com/questions/1337968/reconciling-two-different-definitions-of-constructible-sets/1964351#1964351|title=Reconciling two different definitions of constructible sets|website=math.stackexchange.com|access-date=2016-10-13}}

{{Citation | last1=Atiyah | first1=Michael Francis | author1-link=Michael Atiyah | last2=Macdonald | first2=I.G. | author2-link=Ian G. Macdonald | title=Introduction to Commutative Algebra | publisher=Westview Press | isbn=978-0-201-40751-8 | year=1969 |page=87}}
{{Citation | last=Knight | first=J. T. | authorlink= | title=Commutative Algebra | publisher=Cambridge University Press | isbn=0-521-08193-9 | year=1971 |pages=121–123}}

2 : Commutative algebra|Topology

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