A Choice-free look at algebraic extensions of valuations

Cédric Aïd

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arXiv · 2511.07177

A Choice-free look at algebraic extensions of valuations

Cédric Aïd

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Abstract

In this paper, we study extensions of valuations over algebraic field extensions without the use of the Axiom of Choice. We show a bijection between the extensions of a valuation and the maximal ideals of the relative integral closure of its valuation ring. In the case of a finite extension, we show that these maximal ideals exist. We conclude with an elementary proof of the fundamental inequality.

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Cédric Aïd. 2025-11-10. A Choice-free look at algebraic extensions of valuations. https://arxiv.org/abs/2511.07177

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