2025/11/10 by Cédric Aïd, Aïd, Cédric
Mathematics · Computer Science · #Advanced Topology and Set Theory #Polynomial and algebraic computation #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2511.07177
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.