Prüfer \(v\)-multiplication domains and the completeness of \(w\)-ideals (Q2859349)
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scientific article; zbMATH DE number 6223875
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Prüfer \(v\)-multiplication domains and the completeness of \(w\)-ideals |
scientific article; zbMATH DE number 6223875 |
Statements
7 November 2013
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integrally closed domain and ideal
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\(w\)-cancellation ideal
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PVMD
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\(v\)-ideal
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\(t\)-ideal
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Prüfer \(v\)-multiplication domains and the completeness of \(w\)-ideals (English)
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Let \(R\) be an integral domain with quotient field \(K\). The goal of the paper under review is to give some equivalent characterizations of \(R\) being an integrally closed domain or a Prüfer \(v\)-multiplication domain (PVMD) with the help of some fractional ideals of \(R\) (\(v\)-ideals, \(t\)-ideals, \(w\)-ideals). For example, it is proved that \(R\) is a PVMD if and only if every \(w\)-ideal of \(R\) is integrally closed.
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