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...

Descripción completa

Detalles Bibliográficos
Autores: Alberich Carramiñana, Maria|||0000-0003-2749-4875, Guàrdia Rubies, Jordi|||0000-0003-3287-9358, Nart Vinyals, Enric, Roé Vallvé, Joaquim
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
Descripción
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.