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Ordered Algebraic Structures pp 81–121Cite as

Actions on Archimedean Lattice-Ordered Groups with Strong Unit

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Abstract

This article is an exposition of the basic theory of archimedean lattice-ordered groups with strong unit, endowed with a fixed topological monoid T of actions. We show that every such object is a subdirect product of elementary objects, and show explicitly how to construct all the finite subdirect products. We prove the existence and uniqueness of injective hulls in this category, and describe them to some extent. In particular, we characterize the elementary injectives in terms of idempotent points of the flow compactification of T.

1The first author is grateful to the Caribbean Mathematics Foundation for making possible his attendance of the stimulating conference on ordered algebra held in Curaçao, Netherland Antilles, in June, 1995. This material was presented there.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Denver, Denver, Colorado, 80208, USA

    Richard N. Ball & James N. Hagler

Authors
  1. Richard N. Ball
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  2. James N. Hagler
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Bowling Green State University, Bowling Green, Ohio, USA

    W. Charles Holland

  2. Caribbean Mathematics Foundation, Department of Mathematics, University of Florida, Gainesville, Florida, USA

    Jorge Martinez

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© 1997 Springer Science+Business Media Dordrecht

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Ball, R.N., Hagler, J.N. (1997). Actions on Archimedean Lattice-Ordered Groups with Strong Unit. In: Holland, W.C., Martinez, J. (eds) Ordered Algebraic Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5640-0_4

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  • DOI: https://doi.org/10.1007/978-94-011-5640-0_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6378-4

  • Online ISBN: 978-94-011-5640-0

  • eBook Packages: Springer Book Archive

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