The algebraic theory of valued fields
Michiel Kosters
TL;DR
This paper explores the algebraic extensions of valued fields using Galois theory, providing a mostly known but comprehensive overview that requires no prior valuation knowledge.
Contribution
It offers a unified algebraic Galois-theoretic approach to valued fields, including some new results.
Findings
Most results are well-known in valuation theory.
Some new results are presented.
The approach does not require prior knowledge of valuations.
Abstract
In this exposition we discuss the theory of algebraic extensions of valued fields. Our approach is mostly through Galois theory. Most of the results are well-known, but some are new. No previous knowledge on the theory of valuations is needed.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topology and Set Theory · Algebraic Geometry and Number Theory