A structure theorem for abelian quasi-ordered groups
Logic
2018-10-26 v4
Abstract
We introduce a notion of compatible quasi-ordered groups which unifies valued and ordered abelian groups. It was proved in a paper by Fakhruddin that a compatible quasi-order on a field is always either an order or a valuation. We show here that the group case is more complicated than the field case and describe the general structure of a compatible quasi-ordered abelian group. We also develop a notion of quasi-order-minimality and establish a connection with C-minimality, thus answering a question of F.Delon.
Cite
@article{arxiv.1606.07710,
title = {A structure theorem for abelian quasi-ordered groups},
author = {Gabriel Lehéricy},
journal= {arXiv preprint arXiv:1606.07710},
year = {2018}
}