On algebraically maximal valued fields that are not defectless
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915716162125824 |
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| author | Kuhlmann, Franz-Viktor |
| author_facet | Kuhlmann, Franz-Viktor |
| contents | We use a known example of an algebraically maximal discretely valued field of positive characteristic $p$ which admits purely inseparable extensions of degree $p^2$ with defect $p$ to construct algebraically maximal valued fields of characteristic $p$ as well as of characteristic $0$ and of rank 2 which admit separable extensions of degree $p^2$ with defect $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04872 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On algebraically maximal valued fields that are not defectless Kuhlmann, Franz-Viktor Commutative Algebra 12J10, 12J25 We use a known example of an algebraically maximal discretely valued field of positive characteristic $p$ which admits purely inseparable extensions of degree $p^2$ with defect $p$ to construct algebraically maximal valued fields of characteristic $p$ as well as of characteristic $0$ and of rank 2 which admit separable extensions of degree $p^2$ with defect $p$. |
| title | On algebraically maximal valued fields that are not defectless |
| topic | Commutative Algebra 12J10, 12J25 |
| url | https://arxiv.org/abs/2601.04872 |