Algebra universalis

, Volume 62, Issue 2–3, pp 165–184 | Cite as

A theorem and a question about epicomplete archimedean lattice-ordered groups

  • R. N. Ball
  • A. W. Hager
  • D. G. Johnson
  • A. Kizanis


An archimedean -group is called epicomplete (or universally σ-complete, or sequentially inextensible) if it is divisible, σ-complete and laterally σ-complete. Various characterizations of such G are known in case the G have weak order units. The “theorem” of the title is a characterization of such G which have no weak order unit; it involves the requirement that G have a certain kind of representation. The “question” of the title is whether every epicomplete G has such a representation.

2000 Mathematics Subject Classification

06F20 46A40 54C40 54G05 

Key words and phrases

lattice-ordered group f-ring archimedan representation epicomplete universally σ-complete basically disconnected space P-set 


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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • R. N. Ball
    • 1
  • A. W. Hager
    • 2
  • D. G. Johnson
    • 3
  • A. Kizanis
    • 4
  1. 1.Department of MathematicsUniversity of DenverDenverUSA
  2. 2.Department of MathematicsWesleyan UniversityMiddletownUSA
  3. 3.RamseyUSA
  4. 4.Department of MathematicsWestern New England CollegeSpringfieldUSA

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