A direct proof of a theorem concerning treed overrings (Q1751395)
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scientific article; zbMATH DE number 6873273
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A direct proof of a theorem concerning treed overrings |
scientific article; zbMATH DE number 6873273 |
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A direct proof of a theorem concerning treed overrings (English)
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25 May 2018
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Summary: We improve and provide a direct proof of a theorem that answered a question by Dobbs about treed overrings. More precisely, we show that if \(R\) is an integrally closed local domain and each of its \textit{proper} overrings is treed, then \(R\) is a valuation domain or \(R\) is a PVD with associated valuation overring \(V\) such that \(\mathrm{tr.deg} [V / M : R / M] = 1\).
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