Congruence lattices of free lattices in non-distributive varieties

• Autorzy: Miroslav Ploščica , Jiří Tůma , Friedrich Wehrung
• Języki publikacji: EN

Słowa kluczowe

EN

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 76
• Numer: 2
• Strony: 269-278

Daty

wydano

1998

otrzymano

1997-06-09

poprawiono

1997-10-10

Twórcy

autor

Miroslav Ploščica

• Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 04001 Košice, Slovakia

autor

Jiří Tůma

• Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 00 Praha 8, Czech Republic

autor

Friedrich Wehrung

• Département de Mathématiques Université de Caen 14032 Caen Cedex, France

Bibliografia

• [1] G. M. Bergman, Von Neumann regular rings with tailor-made ideal lattices, unpublished notes, October 1986.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.