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arXiv · 1606.07710

A structure theorem for abelian quasi-ordered groups

Gabriel Lehéricy
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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.

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Gabriel Lehéricy. 2016-06-24. A structure theorem for abelian quasi-ordered groups. https://doi.org/10.1016/j.jpaa.2018.10.016

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