Separation properties in congruence lattices of lattices

Miroslav Ploščica

Colloquium Mathematicae (2000)

  • Volume: 83, Issue: 1, page 71-84
  • ISSN: 0010-1354

Abstract

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We investigate the congruence lattices of lattices in the varieties ℳ n . Our approach is to represent congruences by open sets of suitable topological spaces. We introduce some special separation properties and show that for different n the lattices in ℳ n have different congruence lattices.

How to cite

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Ploščica, Miroslav. "Separation properties in congruence lattices of lattices." Colloquium Mathematicae 83.1 (2000): 71-84. <http://eudml.org/doc/210775>.

@article{Ploščica2000,
abstract = {We investigate the congruence lattices of lattices in the varieties $ℳ _n$. Our approach is to represent congruences by open sets of suitable topological spaces. We introduce some special separation properties and show that for different n the lattices in $ℳ _n$ have different congruence lattices.},
author = {Ploščica, Miroslav},
journal = {Colloquium Mathematicae},
keywords = {algebraic lattice; topological representation; uniform separation; congruence lattices; separation properties},
language = {eng},
number = {1},
pages = {71-84},
title = {Separation properties in congruence lattices of lattices},
url = {http://eudml.org/doc/210775},
volume = {83},
year = {2000},
}

TY - JOUR
AU - Ploščica, Miroslav
TI - Separation properties in congruence lattices of lattices
JO - Colloquium Mathematicae
PY - 2000
VL - 83
IS - 1
SP - 71
EP - 84
AB - We investigate the congruence lattices of lattices in the varieties $ℳ _n$. Our approach is to represent congruences by open sets of suitable topological spaces. We introduce some special separation properties and show that for different n the lattices in $ℳ _n$ have different congruence lattices.
LA - eng
KW - algebraic lattice; topological representation; uniform separation; congruence lattices; separation properties
UR - http://eudml.org/doc/210775
ER -

References

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  3. [3] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott, A Compendium of Continuous Lattices, Springer, 1980. Zbl0452.06001
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  9. [9] M. Ploščica and J. Tůma, Uniform refinements in distributive semilattices, in: Contributions to General Algebra 10 (Klagenfurt '97), Verlag Johannes Heyn, 1998. Zbl0907.06002
  10. [10] M. Ploščica, J. Tůma and F. Wehrung, Congruence lattices of free lattices in nondistributive varieties, Colloq. Math. 76 (1998), 269-278. Zbl0904.06005
  11. [11] H. A. Priestley, Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc. 2 (1970), 186-190. Zbl0201.01802
  12. [12] M. H. Stone, Topological representation of distributive lattices and Brouwerian logics, Čas. Pěst. Mat. Fyz. 67 (1937), 1-25. Zbl0018.00303
  13. [13] F. Wehrung, Non-measurability properties of interpolation vector spaces, Israel J. Math. 103 (1998), 177-206. Zbl0916.06018
  14. [14] F. Wehrung, A uniform refinement property of certain congruence lattices, Proc. Amer. Math. Soc. 127 (1999), 363-370. Zbl0902.06006

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