Polynesian Journal of Mathematics

Volume 1, Issue 4

Okutsu sequences in Henselian valued fields

Enric Nart

Abstract:

For $(K,v)$ a Henselian valued field, let $𝜃\in \overline{K}$ with minimal polynomial $F$ over $K$. Okutsu sequences of $𝜃$ have been defined only when the extension $K\left(𝜃\right)∕K$ is defectless. In this paper, we extend this concept to arbitrary $𝜃\in \overline{K}$ and we show that these objects are essentially equivalent to Okutsu frames of $F$ and to Mac Lane–Vaquié chains of the natural valuation on $K\left[x\right]$ induced by $𝜃$.

Keywords: Defect, Henselian field, Krasner’s constant, Mac Lane–Vaquié chain, main invariant, Okutsu frame, Okutsu sequence, valuation.

Citation:

Enric Nart. Okutsu sequences in Henselian valued fields. Polynesian Journal of Mathematics, Volume 1, Issue 4, Pages 1–27. (Dec. 2024) DOI: 10.69763/polyjmath.1.4

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Milestones:

Received 15 Jul 2024
Revised 20 Nov 2024
Accepted 27 Nov 2024
Published 3 Dec 2024
Communicated by Enrique González Jiménez

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