Filters of lattices with respect to a congruence

M. Sambasiva Rao; Abd El-Mohsen Badawy

Discussiones Mathematicae - General Algebra and Applications (2014)

  • Volume: 34, Issue: 2, page 213-219
  • ISSN: 1509-9415

Abstract

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Some properties of filters on a lattice L are studied with respect to a congruence on L. The notion of a θ-filter of L is introduced and these filters are then characterized in terms of classes of θ. For distributive L, an isomorphism between the lattice of θ-filters of L and the lattice of filters of L / θ is obtained.

How to cite

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M. Sambasiva Rao, and Abd El-Mohsen Badawy. "Filters of lattices with respect to a congruence." Discussiones Mathematicae - General Algebra and Applications 34.2 (2014): 213-219. <http://eudml.org/doc/270727>.

@article{M2014,
abstract = {Some properties of filters on a lattice L are studied with respect to a congruence on L. The notion of a θ-filter of L is introduced and these filters are then characterized in terms of classes of θ. For distributive L, an isomorphism between the lattice of θ-filters of L and the lattice of filters of $L_\{/θ\}$ is obtained.},
author = {M. Sambasiva Rao, Abd El-Mohsen Badawy},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {congruence; filter; closure operator; θ-filter; congruence lattice},
language = {eng},
number = {2},
pages = {213-219},
title = {Filters of lattices with respect to a congruence},
url = {http://eudml.org/doc/270727},
volume = {34},
year = {2014},
}

TY - JOUR
AU - M. Sambasiva Rao
AU - Abd El-Mohsen Badawy
TI - Filters of lattices with respect to a congruence
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2014
VL - 34
IS - 2
SP - 213
EP - 219
AB - Some properties of filters on a lattice L are studied with respect to a congruence on L. The notion of a θ-filter of L is introduced and these filters are then characterized in terms of classes of θ. For distributive L, an isomorphism between the lattice of θ-filters of L and the lattice of filters of $L_{/θ}$ is obtained.
LA - eng
KW - congruence; filter; closure operator; θ-filter; congruence lattice
UR - http://eudml.org/doc/270727
ER -

References

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  1. [1] R. Balbes and P. Dwinger, Distributive Lattices (University of Missouri Press, Columbia, Mo., 1974). 
  2. [2] G. Birkhoff, Lattice Theory (Amer. Math. Soc. Colloq. XXV, Providence, USA, 1967). 
  3. [3] T.S. Blyth, Ideals and filters of pseudo-complemeneted semi-lattices, Proc. Edinburgh Math. Soc. 23 (1980) 301-316. doi: 10.1017/S0013091500003850 Zbl0484.06004
  4. [4] B.A. Davey and H.A. Priestly, Introduction to Lattice and Order (Cambridge University Press, USA, 2002). doi: 10.1017/CBO9780511809088 
  5. [5] G. Grätzer and E.T. Schmidt, Ideals and congruence relations in lattices, Acta Math. Acad. Sci. Hungary 9 (1958) 137-175. doi: 10.1007/BF02023870 Zbl0085.02002
  6. [6] G. Grätzer and E.T. Schmidt, On congruence relations of lattices, Acta Math. Acad. Sci. Hungary 13 (1962) 179-185. doi: 10.1007/BF02033636 Zbl0101.02103
  7. [7] T.P. Speed, Two congruences on distributive lattices, Bulletin de la Societe Royale des Sciences de Liege, 38e (3-4) (1969) 86-95. 

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