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Subgroups and Hulls of Specker Lattice-Ordered Groups

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Abstract

In this article, it will be shown that every ℓ-subgroup of a Specker ℓ-group has singular elements and that the class of ℓ-groups that are ℓ-subgroups of Specker ℓ-group form a torsion class. Methods of adjoining units and bases to Specker ℓ-groups are then studied with respect to the generalized Boolean algebra of singular elements, as is the strongly projectable hull of a Specker ℓ-group.

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References

  1. P. F. Conrad: The hulls of representable ℓ-groups and f-rings. J. Austral. Math. Soc. 16 (1973), 385–415.

    Google Scholar 

  2. P. F. Conrad: Epi-archimedean ℓ-groups. Czechoslovak Math. J. 24 (1974), 192–218.

    Google Scholar 

  3. P. F. Conrad: The hulls of semiprime rings. Czechoslovak Math. J. 28 (1978), 59–86.

    Google Scholar 

  4. P. F. Conrad and M.R. Darnel: Lattice-ordered groups whose lattices determine their additions. Trans. Amer. Math. Soc. 330 (1992), 575–598.

    Google Scholar 

  5. P. F. Conrad and M.R. Darnel: Countably valued lattice-ordered groups. Algebra Universalis 36 (1996), 81–107.

    Google Scholar 

  6. P. F. Conrad and M.R. Darnel: Generalized Boolean algebras in lattice-ordered groups. Order 14 (1998), 295–319.

    Google Scholar 

  7. P. F. Conrad and J. Martinez: Signatures and S-discrete lattice-ordered groups. Algebra Universalis 29 (1992), 521–545.

    Google Scholar 

  8. P. F. Conrad and D. McAlister: The completion of a ℓ-group. J. Austral. Math. Soc. 9 (1969), 182–208.

    Google Scholar 

  9. M. R. Darnel: The Theory of Lattice-ordered Groups. Marcel Dekker, 1995.

  10. M. R. Darnel, M. Giraudet and S. H. McCleary: Uniqueness of the group operation on the lattice of order-automorphisms of the real line. Algebra Universalis 33 (1995), 419–427.

    Google Scholar 

  11. W.C. Holland: Partial orders of the group of automorphisms of the real line. Proc. International Conf. on Algebra, Part 1 (Novosibirsk, 1989), pp. 197–207; Contemp. Math. Vol. 131. Amer. Math. Soc., 1992.

    Google Scholar 

  12. J. Jakubík: Lattice-ordered groups with unique addition must be archimedean. Czechoslovak Math. J. 41(116) (1991), 559–603.

    Google Scholar 

  13. S. Lin: Some Theorems on Lattice-ordered Groups. Dissertation, University of Kansas, 1991

  14. C. Nobeling: Verallgemeinerung eines Satzes von Herrn E. Specker. Invent. Math. 6 (1968), 41–55.

    Google Scholar 

  15. S. Wolfenstein: Contribution è l'étude des groupes reticulés: Extensions archimédiennes, Groupes è valeurs normales. Thesis, Sci. Math. Paris, 1970.

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Authors and Affiliations

  1. Department of Mathematics, P. F. Conrad, University of Kansas, USA

    Paul F. Conrad

  2. Department of Mathematics, Indiana University, South Bend, USA

    Michael R. Darnel

Authors
  1. Paul F. Conrad
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  2. Michael R. Darnel
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Conrad, P.F., Darnel, M.R. Subgroups and Hulls of Specker Lattice-Ordered Groups. Czechoslovak Mathematical Journal 51, 395–413 (2001). https://doi.org/10.1023/A:1013759300701

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