Advertisement

algebra universalis

, Volume 30, Issue 2, pp 241–261 | Cite as

Multipasting of lattices

  • E. Fried
  • G. Grätzer
  • E. T. Schimidt
Article

Abstract

In this paper we introduce a lattice construction, calledmultipasting, which is a common generalization of gluing, pasting, andS-glued sums. We give a Characterization Theorem which generalizes results for earlier constructions. Multipasting is too general to prove the analogues of many known results. Therefore, we investigate in some detail three special cases: strong multipasting, multipasting of convex sublattices, and multipasting with the Interpolation Property.

Keywords

Interpolation Property Characterization Theorem Common Generalization Lattice Construction Early Construction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Day, A. andHerrmann, Ch.,Gluings of modular lattices, Order5 (1988), 85–101.Google Scholar
  2. [2]
    Day, A. andJezek, J.,The Amalgamation Property for varieties of lattices, Trans. Amer. Math. Soc.286 (1984), 251–256.Google Scholar
  3. [3]
    Fried, E. andGrätzer, G.,Partial and free weakly associative lattices, Houston J. Math.24 (1976), 501–512.Google Scholar
  4. [4]
    Fried, E. andGrätzer, G.,Pasting and modular lattices, Proc. Amer. Math. Soc.196 (1989), 885–890.Google Scholar
  5. [5]
    Fried, E. andGrätzer, G.,Pasting infinite lattices, J. Austral. Math. Soc. (Series A)47 (1989), 1–21.Google Scholar
  6. [6]
    Fried, E. andGrätzer, G.,The Unique Amalgamation Property for lattices, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. (1990).Google Scholar
  7. [7]
    Fried, E. Grätzer, G., andLakser, H.,Projective geometries as cover preserving sublattices, Algebra Universalis27 (1990), 270–278.Google Scholar
  8. [8]
    Grätzer, G.,General Lattice Theory, Academic Press, New York, N.Y.; Birkhäuser Verlag, Basel; Akademie Verlag, Berlin, 1978.Google Scholar
  9. [9]
    Hall, M. andDilworth, R. P.,The embedding problem for modular lattices, Ann. of Math.2 (1944), 450–456.Google Scholar
  10. [10]
    Herrmann, Ch.,S-verklebte Summen von Verbänden, Math. Z.130 (1973), 255–274.Google Scholar
  11. [11]
    Slavík, V.,A note on the amalgamation properties in lattice varieties, Comm. Math. Univ. Carolinae21 (1980), 473–478.Google Scholar
  12. [12]
    Schmidt, E. T.,On splitting modular lattices, Colloquia Mathematica Soc. János Bólyai29 (1977), 697–703.Google Scholar
  13. [13]
    Schmidt, E. T.,On finitely projected modular lattices, Acta Math. Acad. Sci. Hungar.39 (1981), 45–51.Google Scholar
  14. [14]
    Schmidt, E. T.,On locally order-polynomially complete modular lattices, Acta Math. Acad. Sci. Hungar.49 (1987), 481–486.Google Scholar
  15. [15]
    Schmidt, E. T.,Pasting and semimodular lattices, Algebra Universalis27 (1990), 595–596.Google Scholar

Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • E. Fried
    • 1
  • G. Grätzer
    • 1
  • E. T. Schimidt
    • 1
  1. 1.Department of MathematicsUniversity of ManitobaWinnipegCanada

Personalised recommendations