On valuation independence and defectless extensions of valued fields

TL;DR

This paper advances the theory of valuation independence, explores its connection with classical valuation concepts, and resolves open questions about defectless extensions, providing new characterizations within various valued field classes.

Contribution

It develops valuation independence theory further, answers open questions on vector space defectless extensions, and extends existing characterizations in valued field classes.

Findings

Resolved two open questions on vector space defectless extensions

Provided new characterizations of defectless extensions in various valued fields

Extended results of Françoise Delon in valuation theory

Abstract

In this article we further develop the theory of valuation independence and study its relation with classical notions in valuation theory such as immediate and defectless extensions. We use this general theory to settle two open questions regarding vector space defectless extensions of valued fields. Additionally, we provide a characterization of such extensions within various classes of valued fields, extending results of Fran\c{c}oise Delon.