Okutsu frames of irreducible polynomials over Henselian fields
For a Henselian valued field ( K , v ) we establish a complete parallelism between the arithmetic properties of irreducible polynomials F ¿ K [ x ] , encoded by their Okutsu frames, and the valuation-theoretic properties of their induced valuations v F on K [ x ] , encoded by their Mac Lane–Vaquié c...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/443033 |
| Acceso en línea: | https://hdl.handle.net/2117/443033 https://dx.doi.org/10.1142/S0219498826501823 |
| Access Level: | acceso abierto |
| Palabra clave: | Henselian field Key polynomial Mac Lane–Vaquié chain Okutsu frame Valuation Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Anells i àlgebres Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis |
| Sumario: | For a Henselian valued field ( K , v ) we establish a complete parallelism between the arithmetic properties of irreducible polynomials F ¿ K [ x ] , encoded by their Okutsu frames, and the valuation-theoretic properties of their induced valuations v F on K [ x ] , encoded by their Mac Lane–Vaquié chains. This parallelism was only known for defectless irreducible polynomials. |
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