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/

[1] R. Balbes and P. Dwinger, Distributive Lattices (University of Missouri Press, Columbia, Mo., 1974).

[2] G. Birkhoff, Lattice Theory (Amer. Math. Soc. Colloq. XXV, Providence, USA, 1967).

[3] T.S. Blyth, Ideals and filters of pseudo-complemeneted semi-lattices, Proc. Edinburgh Math. Soc. 23 (1980) 301-316. doi: 10.1017/S0013091500003850

[4] B.A. Davey and H.A. Priestly, Introduction to Lattice and Order (Cambridge University Press, USA, 2002). doi: 10.1017/CBO9780511809088

[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

[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

[7] T.P. Speed, Two congruences on distributive lattices, Bulletin de la Societe Royale des Sciences de Liege, 38e (3-4) (1969) 86-95.