Skip to main content
SpringerLink
Log in

Strong Projectability of Lattice Ordered Groups

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

In this paper we prove that the lateral completion of a projectable lattice ordered group is strongly projectable. Further, we deal with some properties of Specker lattice ordered groups which are related to lateral completeness and strong projectability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. J. Bernau: The lateral completion of an arbitrary lattice group. J. Austral. Math. Soc. 19 (1975), 263–289.

    MATH  MathSciNet  Google Scholar 

  2. S. J. Bernau: Lateral and Dedekind completion of archimedean lattice groups. J. London Math. Soc. 12 (1976), 320–322.

    MATH  MathSciNet  Google Scholar 

  3. R. D. Bleier: The SP-hull of a lattice-ordered group. Canadian J. Math. 26 (1974), 866–878.

    MATH  MathSciNet  Google Scholar 

  4. R. D. Bleier: The orthocompletion of a lattice-ordered group. Indagationes Math. 38 (1976), 1–7.

    MathSciNet  Google Scholar 

  5. D. Byrd and T. J. Lloyd: A note on lateral completion in lattice ordered groups. J. London Math. Soc. 1 (1969), 358–362.

    MathSciNet  MATH  Google Scholar 

  6. D. A. Chambless: Representation of the projectable and strongly projectable hulls of a lattice ordered group. Proc. Amer. Math. Soc. 19 (1975), 263–289.

    Google Scholar 

  7. P. F. Conrad: Lateral completion of lattice ordered groups. Proc. London Math. Soc. 19 (1969), 444–480.

    MATH  MathSciNet  Google Scholar 

  8. P. F. Conrad: Lattice Ordered Groups. Tulane University, 1970.

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  12. M. R. Darnel: The Theory of Lattice Ordered Groups. Marcel Dekker, New York-Basel, 1995.

    Google Scholar 

  13. J. Jakubik: Representations and extensions of ℓ-groups. Czechoslovak Math. J. 13 (1963), 267–282. (In Russian.)

    MATH  MathSciNet  Google Scholar 

  14. J. Jakubik: Lateral and Dedekind completions of strongly projectable lattice ordered groups. Czechoslovak Math. J 47 (1997), 511–523.

    MATH  MathSciNet  Google Scholar 

  15. J. Jakubik: Orthogonal hull of a strongly projectable lattice ordered group. Czechoslovak Math. J. 28 (1978), 484–504.

    MATH  MathSciNet  Google Scholar 

  16. J. Jakubik: Torsion classes of Specker lattice ordered groups. Czechoslovak Math. J. 52 (2002), 469–482.

    MATH  MathSciNet  Google Scholar 

  17. J. Jakubik: Konvexe Ketten in ℓ-Gruppen. Cas. pest. mat. 84 (1959), 53–63.

    MATH  MathSciNet  Google Scholar 

  18. K. Keimel: Representation de groupes et d'anneaux reticules par des sections dans des faisceaux. PhD. Thesis, Universite de Paris, 1970.

  19. G. Ya. Rotkovich: On some kinds of completeness in archimedean lattice ordered groups. Funkc. anal. 9 (1977), 138–143. (In Russian.)

    MATH  Google Scholar 

  20. R. Sikorski: Boolean Algebras. Second Edition, Springer-Verlag, Berlin, 1964.

    MATH  Google Scholar 

  21. E. C. Smith Jr. and A. Tarski: Higher degrees of distributivity and completeness in Boolean algebras. Trans. Amer. Math. Soc. 84 (1957), 230–257.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Matematicky ustav SAV, Gresakova 6, 040 01, Kosice, Slovakia

    Jan Jakubik

Authors
  1. Jan Jakubik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by VEGA grant 2/1131/21.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jakubik, J. Strong Projectability of Lattice Ordered Groups. Czech Math J 55, 957–973 (2005). https://doi.org/10.1007/s10587-005-0080-3

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10587-005-0080-3

Keywords

Search

Navigation