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Preordered groups and valued fields
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abstract
We study algebraic, combinatorial and topological properties of the set of preorders on a group, and the set of valuations on a field. We show strong analogies between these two kinds of sets and develop a dictionary for these ones. Among the results we make a detailed study of the set of preorders on $\mathbb Z^n$. We also prove that the set of valuations on a countable field of transcendence degree at least 2 is an ultrametric Cantor set.
Forward citations
Cited by 2 Pith papers
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Spaces of left-preorders on free products
Left-preorder spaces of free products have no isolated elements; when the factors are finitely generated, every nonempty such space is a Cantor set.
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The space of Conradian left-preorders
For any group, the space of Conradian left-preorders is either finite or uncountable, and finiteness is characterized by the existence of a unique finite rational series without abelian jumps.
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