A general theory of structure spaces with applications to spaces of prime ideals (Q1179769)
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scientific article; zbMATH DE number 25317
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A general theory of structure spaces with applications to spaces of prime ideals |
scientific article; zbMATH DE number 25317 |
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A general theory of structure spaces with applications to spaces of prime ideals (English)
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27 June 1992
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Let \(R\) be a ring, possibly without an identity element. The join of the Zariski topology on \(\text{Spec}(R)\) and its dual is called the patch topology and is studied here in great detail. In particular the closure in the patch topology of various subspaces of \(\text{Spec}(R)\) is determined such as \(\text{MinSpec}(R)=\) the space of minimal prime ideals and \(\text{MaxSpec}(R)=\) the space of maximal prime ideals. Among other things it is also shown that the patch topology on \(2^ R\) is a compact zero-dimensional Hausdorff space. Its compact subsets are characterized.
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Zariski topology
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patch topology
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minimal prime ideals
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maximal prime ideals
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compact zero-dimensional Hausdorff space
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