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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.
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Abstract

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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

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