Filters of lattices with respect to a congruence
Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 2, pp. 213-219
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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.
Keywords:
congruence, filter, closure operator, θ-filter, congruence lattice
@article{DMGAA_2014_34_2_a6,
author = {Sambasiva Rao, M. and El-Mohsen Badawy, Abd},
title = {Filters of lattices with respect to a congruence},
journal = {Discussiones Mathematicae. General Algebra and Applications},
pages = {213--219},
publisher = {mathdoc},
volume = {34},
number = {2},
year = {2014},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGAA_2014_34_2_a6/}
}
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Sambasiva Rao, M.; El-Mohsen Badawy, Abd. Filters of lattices with respect to a congruence. Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 2, pp. 213-219. http://geodesic.mathdoc.fr/item/DMGAA_2014_34_2_a6/