Totally ramified subfields of $p$-algebras over discrete valued fields with imperfect residue
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909456233660416 |
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| author | Srimathy, S. |
| author_facet | Srimathy, S. |
| contents | Let $K$ be a complete discrete valued field of characteristic $p$ with residue $k$ which is not necessarily perfect. We prove the Conjecture in \cite{cs} that a $p$-algebra over $K$ contains a totally ramified cyclic maximal subfield if it contains a totally ramified purely inseparable maximal subfield provided $k$ satisfies some conditions on its $p$-rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17497 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Totally ramified subfields of $p$-algebras over discrete valued fields with imperfect residue Srimathy, S. Rings and Algebras Number Theory 16K20, 16W60, 12F15, 11S15 Let $K$ be a complete discrete valued field of characteristic $p$ with residue $k$ which is not necessarily perfect. We prove the Conjecture in \cite{cs} that a $p$-algebra over $K$ contains a totally ramified cyclic maximal subfield if it contains a totally ramified purely inseparable maximal subfield provided $k$ satisfies some conditions on its $p$-rank. |
| title | Totally ramified subfields of $p$-algebras over discrete valued fields with imperfect residue |
| topic | Rings and Algebras Number Theory 16K20, 16W60, 12F15, 11S15 |
| url | https://arxiv.org/abs/2406.17497 |