Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T13:36:24.347Z Has data issue: false hasContentIssue false
  • English
  • Français

The root system of primes of a Hahn group

Part of: Ordered structures

Published online by Cambridge University Press:  09 April 2009

Marlow Anderson  and
Otis Kenny
Marlow Anderson
Affiliation:
Department of Mathematical Sciences Indiana University-Purdue Universityat Fort Wayne 2101 Coliseum Boulevard East Fort Wayne, Indiana 46805, U.S.A.
Otis Kenny
Affiliation:
Department of Mathematics Boise State UniversityBoise, Idaho 83725, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let δ be a root system and let V be the Hahn group of real-valued functions on δ Then δ can be order-embedded into P(δ), the root system of prime l-ideals of V. In this note we identify P(δ) in terms of δ without explicit reference to V, up to the convex subgroup structure of the additive groups of real closed η1-fields. In particular, we characterize the minimal prime 1-ideals of V in terms of δ by an ultrafilter construction which generalizes the well-known method when δ is trivially ordered.

MSC classification

Secondary: 06F20: Ordered abelian groups, Riesz groups, ordered linear spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 1 , February 1980 , pp. 17 - 28
Copyright
Copyright © Australian Mathematical Society 1980

References

Bigard, A., Keimel, K. and Wolfenstein, S. (1977), Groupes et anneaux réticules (Springer-Verlag, Berlin).CrossRefGoogle Scholar
Conrad, P. (1970), Lattice-ordered groups (Tulane Library, New Orleans).Google Scholar
Conrad, P. (1978), ‘Minimal prime subgroups of lattice-ordered groups’, preprint.Google Scholar
Conrad, P., Harvey, J. and Holland, C. (1963), ‘The Hahn embedding theorem for lattice-ordered groups’, Trans. Amer. Math. Soc. 108, 143–169.CrossRefGoogle Scholar
Conrad, P. and McAlister, D. (1969), ‘The completion of a lattice-ordered group’, J. Austral. Math. Soc. 9, 182–208.CrossRefGoogle Scholar
Gillman, L. and Jerison, M. (1960), Rings of continuous functions (van Nostrand, Princeton).CrossRefGoogle Scholar