Finitely presented, coherent, and ultrasimplicial ordered abelian groups

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dc.creatorCaillot, Jean-François
dc.creatorWehrung, Friedrich
dc.date2005-01-25
dc.date.accessioned2026-07-07T05:16:21Z
dc.date.available2026-07-07T05:16:21Z
dc.descriptionWe study notions such as finite presentability and coherence, for partially ordered abelian groups and vector spaces. Typical results are the following: (i) A partially ordered abelian group G is finitely presented if and only if G is finitely generated as a group, the positive cone G^+ is well-founded as a partially ordered set, and the set of minimal elements of (G^+)-{0} is finite. (ii) Torsion-free, finitely presented partially ordered abelian groups can be represented as subgroups of some Z^n, with a finitely generated submonoid of (Z+)^n as positive cone. (iii) Every unperforated, finitely presented partially ordered abelian group is Archimedean. Further, we establish connections with interpolation. In particular, we prove that a divisible dimension group G is a directed union of simplicial subgroups if and only if every finite subset of G is contained into a finitely presented ordered subgroup.
dc.identifierhttps://arxiv.org/abs/math/0501432
dc.identifierhttp://arxiv.org/abs/math/0501432
dc.identifierSemigroup Forum 61 (2000) 116--137
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73959
dc.subjectGeneral Mathematics
dc.subject06F20, 06F25, 15A39, 12J15
dc.titleFinitely presented, coherent, and ultrasimplicial ordered abelian groups
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