Definable henselian valuations on dp-minimal real fields
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912072376254464 |
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| author | Krapp, Lothar Sebastian Kuhlmann, Salma Vogel, Lasse |
| author_facet | Krapp, Lothar Sebastian Kuhlmann, Salma Vogel, Lasse |
| contents | We give an explicit algebraic characterisation of all definable henselian valuations on a dp-minimal real field. Additionally we characterise all dp-minimal real fields that admit a definable henselian valuation with real closed residue field. We do so by first proving this for the more general setting of almost real closed fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10344 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Definable henselian valuations on dp-minimal real fields Krapp, Lothar Sebastian Kuhlmann, Salma Vogel, Lasse Logic Commutative Algebra Primary 12J10 03C45, Secondary 03C60 03C40 13J30 16W60 12L12 We give an explicit algebraic characterisation of all definable henselian valuations on a dp-minimal real field. Additionally we characterise all dp-minimal real fields that admit a definable henselian valuation with real closed residue field. We do so by first proving this for the more general setting of almost real closed fields. |
| title | Definable henselian valuations on dp-minimal real fields |
| topic | Logic Commutative Algebra Primary 12J10 03C45, Secondary 03C60 03C40 13J30 16W60 12L12 |
| url | https://arxiv.org/abs/2410.10344 |