On the lattice of n-filters of an LM n-algebra
Dumitru Buşneag ; Florentina Chirteş
Open Mathematics, Tome 5 (2007), p. 470-483 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

For an n-valued Łukasiewicz-Moisil algebra L (or LM n-algebra for short) we denote by F n(L) the lattice of all n-filters of L. The goal of this paper is to study the lattice F n(L) and to give new characterizations for the meet-irreducible and completely meet-irreducible elements on F n(L).

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:269290 
@article{bwmeta1.element.doi-10_2478_s11533-007-0012-6,
     author = {Dumitru Bu\c sneag and Florentina Chirte\c s},
     title = {On the lattice of n-filters of an LM n-algebra},
     journal = {Open Mathematics},
     volume = {5},
     year = {2007},
     pages = {470-483},
     zbl = {1129.06010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0012-6}
}

Dumitru Buşneag; Florentina Chirteş. On the lattice of n-filters of an LM n-algebra. Open Mathematics, Tome 5 (2007) pp. 470-483. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0012-6/

[1] R. Balbes and Ph. Dwinger: Distributive Lattices, University of Missouri Press, 1974.

[2] G. Birkhoff: Lattice theory, (3rd Edition, 2nd Printing), Amer. Math. Soc., Colloquium Publications XXV, 1973.

[3] V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu: Łukasiewicz-Moisil Algebras, North Holland, 1991.

[4] R. Cignoli: “Boolean multiplicative closures I y II”, P. Jpn. Acad., Vol. 42, (1965), pp. 1168–1174. http://dx.doi.org/10.3792/pja/1195521767 | Zbl 0149.25703

[5] R. Cignoli: Algebras de Moisil de orden n, Thesis (PhD), Universidad National del Sur Bahía Blanca, 1969.

[6] R. Cignoli: Moisil Algebras, Notas de Lógica Matemática, 27, Univ. National del Sur, Bahía Blanca, 1970.

[7] G. Georgescu and M. Ploščcica: “Values and minimal spectrum of an algebric lattice”, Math. Slovaca, Vol. 52, (2002), pp. 247–253.

[8] G. Grätzer: Lattice theory, W. H. Freeman and Company, San Francisco, 1979.

[9] A. Iorgulescu: (1+0)-valued Łuksiewicz-Moisil algebras with negation, Thesis (PhD), Univ. of Bucharest, 1984.

[10] Gr.C. Moisil: “Recherches sur les logiques non-chrysippienns,” An. Sci. Univ. Jassy, Vol. 26, (1940), pp. 195–232.

[11] Gr.C. Moisil: “Applicationi dell’algebra alle calculatrici moderne”, In: Atti 2 a Reunione del Groupement des Math. d’Expression Latine, 26.IX-3.X.1961, Ed. Cremonese, Roma.

[12] Gr.C. Moisil: “Łukasiewiczian algebras”, Preprint: Computing Center, Univ. Bucharest, 1968, pp. 311–324.

[13] A. Monteiro: ”L’arithmétique des filtres et les espaces topologiques”, In:’ it Segundo Symposium Americano de Mat., Centro de Cooperatión Científica de la UNESCO para América Latina, Montevideo, 1954, pp. 129–162.

[14] A. Monteiro: “Construction des algèbres de Łukasiewicz trivalentes dans les algèbres de Boole monadiques”, Math. Japon. Vol. 12, (1967), pp. 1–23. | Zbl 0165.30903