Nonfinite heights (Q2785921)
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scientific article; zbMATH DE number 983062
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonfinite heights |
scientific article; zbMATH DE number 983062 |
Statements
5 March 1998
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valuative dimension
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valuative height
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height
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integral domain
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Krull dimension
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0.79723537
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Nonfinite heights (English)
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The concepts of dimension (valuative dimension) of a ring, height (valuative height) of a prime ideal \({\mathfrak p}\) of an integral domain \(R\) as an ordinal number are introduced. The results that hold for prime ideals in the finite case are shown to hold in the transfinite case as well. There are a number of examples to illustrate the results and the concepts introduced in this paper. For instance, examples of a ring of Krull dimension \(\alpha\) for each \(\alpha\) as also a ring without any Krull dimension are given.NEWLINENEWLINEFor the entire collection see [Zbl 0855.00015].
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