MacLane-Vaqui\'e chains and Valuation-Transcendental Extensions

TL;DR

This paper explores the relationship between complete sets of ABKPs and MacLane-Vaquié chains in the context of valuation extensions of valued fields, providing a theoretical framework for understanding valuation-transcendental extensions.

Contribution

It establishes a connection between ABKPs and MacLane-Vaquié chains for valuation extensions, extending the theory to arbitrary rank valued fields.

Findings

Established a link between ABKPs and MacLane-Vaquié chains.

Extended valuation theory to arbitrary rank valued fields.

Provided new insights into valuation-transcendental extensions.

Abstract

In this paper, for a valued field $(K, v)$ of arbitrary rank and an extension $w$ of $v$ to $K(X),$ we give a connection between complete sets of ABKPs for $w$ and MacLane-Vaqui\'e chains of $w.$