Filters of lattices with respect to a congruence

• Autorzy: M. Sambasiva Rao , Abd El-Mohsen Badawy
• Języki publikacji: EN

Abstrakty

EN

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

EN

congruence; filter; closure operator; θ-filter; congruence lattice

Kategorie tematyczne

• 06D99: None of the above, but in this section

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2014
• Tom: 34
• Numer: 2
• Strony: 213-219

Daty

wydano

2014

otrzymano

2014-09-21

poprawiono

2014-10-05

poprawiono

2014-10-20

Twórcy

autor

M. Sambasiva Rao

• Department of Mathematics, M.V.G.R. College of Engineering, Chintalavalasa Vizianagaram, Andhra Pradesh, India-535005

autor

Abd El-Mohsen Badawy

• 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.

Identyfikatory

DOI

10.7151/dmgaa.1223