Congruence lattices of free lattices in non-distributive varieties

Miroslav Ploščica; Jiří Tůma; Friedrich Wehrung

Colloquium Mathematicae (1998)

  • Volume: 76, Issue: 2, page 269-278
  • ISSN: 0010-1354

How to cite

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Ploščica, Miroslav, Tůma, Jiří, and Wehrung, Friedrich. "Congruence lattices of free lattices in non-distributive varieties." Colloquium Mathematicae 76.2 (1998): 269-278. <http://eudml.org/doc/210565>.

@article{Ploščica1998,
author = {Ploščica, Miroslav, Tůma, Jiří, Wehrung, Friedrich},
journal = {Colloquium Mathematicae},
keywords = {diamond; congruence splitting lattice; Kuratowski's Theorem; Uniform Refinement Property; congruence lattice; pentagon; uniform refinement property; Kuratowski's theorem; nondistributive variety of lattices; free lattice; von Neumann regular ring},
language = {eng},
number = {2},
pages = {269-278},
title = {Congruence lattices of free lattices in non-distributive varieties},
url = {http://eudml.org/doc/210565},
volume = {76},
year = {1998},
}

TY - JOUR
AU - Ploščica, Miroslav
AU - Tůma, Jiří
AU - Wehrung, Friedrich
TI - Congruence lattices of free lattices in non-distributive varieties
JO - Colloquium Mathematicae
PY - 1998
VL - 76
IS - 2
SP - 269
EP - 278
LA - eng
KW - diamond; congruence splitting lattice; Kuratowski's Theorem; Uniform Refinement Property; congruence lattice; pentagon; uniform refinement property; Kuratowski's theorem; nondistributive variety of lattices; free lattice; von Neumann regular ring
UR - http://eudml.org/doc/210565
ER -

References

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  1. [1] G. M. Bergman, Von Neumann regular rings with tailor-made ideal lattices, unpublished notes, October 1986. 
  2. [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. [3] G. Grätzer and E. T. Schmidt, On congruence lattices of lattices, Acta Math. Acad. Sci. Hungar. 13 (1962), 179-185. Zbl0101.02103
  4. [4] G. Grätzer and E. T. Schmidt, Congruence-preserving extensions of finite lattices to sectionally complemented lattices, Proc. Amer. Math. Soc., to appear. Zbl0923.06003
  5. [5] K. Kuratowski, Sur une caractérisation des alephs, Fund. Math. 38 (1951), 14-17. Zbl0044.27302
  6. [6] E. T. Schmidt, Zur Charakterisierung der Kongruenzverbände der Verbände, Mat. Časopis Sloven. Akad. Vied 18 (1968), 3-20. Zbl0155.35102
  7. [7] M. Tischendorf, On the representation of distributive semilattices, Algebra Universalis 31 (1994), 446-455. Zbl0794.06003
  8. [8] F. Wehrung, Non-measurability properties of interpolation vector spaces, Israel J. Math., to appear. 
  9. [9] F. Wehrung, A uniform refinement property of certain congruence lattices, Proc. Amer. Math. Soc., to appear. 

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