ArticleOriginal scientific text

Title

Congruence lattices of free lattices in non-distributive varieties

Authors 1, 2, 3

Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 04001 Košice, Slovakia
  2. Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 00 Praha 8, Czech Republic
  3. Département de Mathématiques Université de Caen 14032 Caen Cedex, France

Keywords

diamond, congruence splitting lattice, Kuratowski's Theorem, Uniform Refinement Property, congruence lattice, pentagon

Bibliography

  1. G. M. Bergman, Von Neumann regular rings with tailor-made ideal lattices, unpublished notes, October 1986.
  2. G. Grätzer, General Lattice Theory, Pure and Appl. Math. 75, Academic Press, New York; Lehrbücher Monograph. Gebiete Exakt. Wiss. Math. Reihe 52, Birkhäuser, Basel, 1978.
  3. G. Grätzer and E. T. Schmidt, On congruence lattices of lattices, Acta Math. Acad. Sci. Hungar. 13 (1962), 179-185.
  4. G. Grätzer and E. T. Schmidt, Congruence-preserving extensions of finite lattices to sectionally complemented lattices, Proc. Amer. Math. Soc., to appear.
  5. K. Kuratowski, Sur une caractérisation des alephs, Fund. Math. 38 (1951), 14-17.
  6. E. T. Schmidt, Zur Charakterisierung der Kongruenzverbände der Verbände, Mat. Časopis Sloven. Akad. Vied 18 (1968), 3-20.
  7. M. Tischendorf, On the representation of distributive semilattices, Algebra Universalis 31 (1994), 446-455.
  8. F. Wehrung, Non-measurability properties of interpolation vector spaces, Israel J. Math., to appear.
  9. F. Wehrung, A uniform refinement property of certain congruence lattices, Proc. Amer. Math. Soc., to appear.
Pages:
269-278
Main language of publication
English
Received
1997-06-09
Accepted
1997-10-10
Published
1998
Exact and natural sciences