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Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
213-219
Opis fizyczny
Daty
wydano
2014
otrzymano
2014-09-21
poprawiono
2014-10-05
poprawiono
2014-10-20
Twórcy
autor
- Department of Mathematics, M.V.G.R. College of Engineering, Chintalavalasa Vizianagaram, Andhra Pradesh, India-535005
autor
- Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
Bibliografia
- [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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1223