Abstract key polynomials and distinguished pairs

Sneha Mavi; Anuj Bishnoi

arXiv:2112.15123·math.AC·January 3, 2022

Abstract key polynomials and distinguished pairs

Sneha Mavi, Anuj Bishnoi

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TL;DR

This paper explores the use of abstract key polynomials to analyze extensions of valuations in henselian valued fields, leading to the development of distinguished pairs and chains.

Contribution

It introduces a novel approach using abstract key polynomials to construct distinguished pairs and chains in valuation extensions of henselian fields.

Findings

01

Established a method to obtain distinguished pairs from abstract key polynomials.

02

Developed saturated distinguished chains in valuation extensions.

03

Applicable to fields of arbitrary rank.

Abstract

In this paper, for a henselian valued field $(K, v)$ of arbitrary rank and an extension $w$ of $v$ to $K (X),$ we use abstract key polynomials for $w$ to obtain distinguished pairs and saturated distinguished chains.

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Taxonomy

TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons