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Preprint Number 1061

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1061. Gabriel Lehéricy
A structure theorem for abelian quasi-ordered groups

Submission date: 24 June 2016


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.

Mathematics Subject Classification: 06

Keywords and phrases: ordered groups, valued groups, C-groups, quasi-orders

Full text arXiv 1606.07710: pdf, ps.

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