Geodesic
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 
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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/