Skip to main content
SpringerLink
Log in

On a characterization of lattices by the betweenness relation —on a problem of M. Kolibiar

  • Published:
algebra universalis Aims and scope Submit manuscript

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

References

  1. Altwegg, M.,Zur Axiomatik der teilweise geordneten Mengen. Comment. Math. Helv.24 (1950), 149–155.

    Google Scholar 

  2. Birkhoff, G.,Lattice Theory. Amer. Math. Soc. Colloq. Publ. Vol. 25, 1967, 3rd ed., Providence, R.I.

  3. Burris, S. andSankappanavar, H. P.,A Course in Universal Algebra. Springer-Verlag, New York, 1981.

    Google Scholar 

  4. Cibulskis, J. M.,A characterization of the lattice orderings on a set which induce a given betweenness. J. London Math. Soc (2)1 (1969), 480–482.

    Google Scholar 

  5. Kelly, L. M.,The geometry of normed lattices. Duke Math. J.19 (1952), 661 -669.

    Google Scholar 

  6. Kolibiar, M.,On betweenness relations in lattices. Mat.-Fyz. Časopis SAV5 (1955), 162–171 (Slovak).

    Google Scholar 

  7. Kolibiar, M.,A ternary operation in lattices. Czechoslov. Math. J.6 (81) (1956), 318–329 (Russian).

    Google Scholar 

  8. Kolibiar, M.,Charakterisierung der Verbände durch die Relation “zwischen”. Zeitschr. f. math. Logik und Grundlagen d. Math.4 (1958), 89–100.

    Google Scholar 

  9. Pitcher, E. andSmiley, M. F.,Transitivities of betweenness. Trans. Amer. Math. Soc.52 (1942), 95–114.

    Google Scholar 

  10. Smiley, M. F. andTransue, W. R.,Applications of transitivities of betweenness in lattice theory. Bull. Amer. Math. Soc.49 (1943), 280–287.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Stefánikova 49, 814 73, Bratislava, Czechoslovakia

    Jarmila Hedlíková & Tibor Katrinák

  2. Department of Algebra and Number Theory Mlynská Dolina, Komenský University, 842 15, Bratislava, Czechoslovakia

    Jarmila Hedlíková & Tibor Katrinák

Authors
  1. Jarmila Hedlíková
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tibor Katrinák
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hedlíková, J., Katrinák, T. On a characterization of lattices by the betweenness relation —on a problem of M. Kolibiar. Algebra Universalis 28, 389–400 (1991). https://doi.org/10.1007/BF01191088

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01191088

Keywords

Search

Navigation