Publication

Okutsu frames of irreducible polynomials over Henselian fields

Journal Article (2026)

Journal

Journal of Algebra and Its Applications

Doc link

https://doi.org/10.1142/S0219498826501823

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Authors

Abstract

For a Henselian valued field (K,v) we establish a complete parallelism between the arithmetic properties of irreducible polynomials F in K[x], encoded by their Okutsu frames, and the valuation-theoretic properties of their induced valuations vF on K[x], encoded by their Mac Lane–Vaquié chains. This parallelism was only known for defectless irreducible polynomials.

Categories

automation, pattern recognition.

Author keywords

Henselian field, key polynomial, Mac Lane–Vaquié chain, Okutsu frame, valuation

Scientific reference

M. Alberich-Carramiñana, J. Guàrdia, E. Nart and J. Roé. Okutsu frames of irreducible polynomials over Henselian fields. Journal of Algebra and Its Applications, 2026, to appear.