A Choice-free look at algebraic extensions of valuations
Commutative Algebra
2025-11-11 v1
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.
Cite
@article{arxiv.2511.07177,
title = {A Choice-free look at algebraic extensions of valuations},
author = {Cédric Aïd},
journal= {arXiv preprint arXiv:2511.07177},
year = {2025}
}
Comments
20 pages, 0 figures