# Trichotomy for positive cones and a maximality counterexample

@inproceedings{Astier2021TrichotomyFP, title={Trichotomy for positive cones and a maximality counterexample}, author={Vincent Astier and Thomas Unger}, year={2021} }

In [4] we developed the theory of positive cones on finite-dimensional simple algebras with involution, inspired by the classical Artin-Schreier theory of orderings on fields, and based on the notion of signatures of hermitian forms [1]. In a subsequent paper [3], we developed the associated “valuation theory”, based on Tignol-Wadsworth gauges [7, 8, 9]. In this short note, we present the following two additional results: (1) Whereas positive cones on fields correspond to total order relations…

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