On the lattice of n-filters of an LM n-algebra
Dumitru Buşneag; Florentina Chirteş
Open Mathematics (2007)
- Volume: 5, Issue: 3, page 470-483
- ISSN: 2391-5455
Access Full Article
top
Abstract
topHow to cite
topDumitru Buşneag, and Florentina Chirteş. "On the lattice of n-filters of an LM n-algebra." Open Mathematics 5.3 (2007): 470-483. <http://eudml.org/doc/269290>.
@article{DumitruBuşneag2007,
abstract = {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).},
author = {Dumitru Buşneag, Florentina Chirteş},
journal = {Open Mathematics},
keywords = {LMn-algebra; n-filter; prime n-filter; meet-irreducible n-filter; completely meet-irreducible n-filter},
language = {eng},
number = {3},
pages = {470-483},
title = {On the lattice of n-filters of an LM n-algebra},
url = {http://eudml.org/doc/269290},
volume = {5},
year = {2007},
}
TY - JOUR
AU - Dumitru Buşneag
AU - Florentina Chirteş
TI - On the lattice of n-filters of an LM n-algebra
JO - Open Mathematics
PY - 2007
VL - 5
IS - 3
SP - 470
EP - 483
AB - 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).
LA - eng
KW - LMn-algebra; n-filter; prime n-filter; meet-irreducible n-filter; completely meet-irreducible n-filter
UR - http://eudml.org/doc/269290
ER -
References
top- [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 Zbl0149.25703
- [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. Zbl0165.30903
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.