MODNET
Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1061

Preprint Number 1061

Previous Next Preprint server


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

Submission date: 24 June 2016

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.

Mathematics Subject Classification: 06

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

Full text arXiv 1606.07710: pdf, ps.


Last updated: July 1 2016 12:08 Please send your corrections to: