Closure Łukasiewicz algebras
Abad Manuel ; Cimadamore Cecilia ; Díaz Varela José ; Rueda Laura ; Suardíaz Ana
Open Mathematics, Tome 3 (2005), p. 215-227 / Harvested from The Polish Digital Mathematics Library

In this paper, the variety of closure n-valued Łukasiewicz algebras, that is, Łukasiewicz algebras of order n endowed with a closure operator, is investigated. The lattice of subvarieties in the particular case in which the open elements form a three-valued Heyting algebra is obtained.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:268692
@article{bwmeta1.element.doi-10_2478_BF02479197,
     author = {Abad Manuel and Cimadamore Cecilia and D\'\i az Varela Jos\'e and Rueda Laura and Suard\'\i az Ana},
     title = {Closure \L ukasiewicz algebras},
     journal = {Open Mathematics},
     volume = {3},
     year = {2005},
     pages = {215-227},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02479197}
}
Abad Manuel; Cimadamore Cecilia; Díaz Varela José; Rueda Laura; Suardíaz Ana. Closure Łukasiewicz algebras. Open Mathematics, Tome 3 (2005) pp. 215-227. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02479197/

[00000] [1] M. Abad: Estructuras cíclica y monádica de un álgebra de Lukasiewicz n-valente, Notas de Lógica Matemática, Vol. 36, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca, 1988.

[00001] [2] M. Abad and J.P. Díaz Varela: “Free Algebras in the Variety of Three-valued Closure Algebras”, J. Austral. Math. Soc. Vol. 72, (2002), pp. 181–197. http://dx.doi.org/10.1017/S1446788700003839

[00002] [3] R. Balbes and P. Dwinger: Distributive Lattices, University of Missouri Press, Columbia, MO, 1974.

[00003] [4] G. Bezhanishvili: “Locally finite varieties”, Algebra Universais 46, Vol. 4, 2001, pp. 531–548. http://dx.doi.org/10.1007/PL00000358

[00004] [5] W. Blok: Varieties of interior algebras, Thesis (Ph.D.), University of Amsterdam, 1976.

[00005] [6] V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu: Lukasiewicz-Moisil Algebras, North Holland, 1991.

[00006] [7] R. Cignoli: Moisil Algebras, Notas de Lógica Matemática, Vol. 27, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca, 1970.

[00007] [8] B.A. Davey: “On the lattice of subvarieties”, Houston J. Math., Vol. 5, (1979), pp. 183–192.

[00008] [9] J.P. Díaz Varela: Algebras de Clausura y su Estructura Simétrica, Tesis (Ph.D.), Bahía Blanca, Argentina, 1997.

[00009] [10] L. Iturrioz: “Łukasiewicz and Symmetrical Heyting Algebras”, ZML, Vol. 23(2), (1977), pp. 131–136.

[00010] [11] L. Iturrioz: “Two characteristic properties of three-valued Lukasiewicz algebras” Rep. Math. Logic, Vol. 8, (1977), pp. 63–69.

[00011] [12] Gr.C. Moisil: “Notes sur les logiques non-chrysippiennes”, Ann. Sci. Univ. Jassy, Vol. 27, (1941), pp. 86–98.

[00012] [13] A. Monteiro: L'aritmétique des filtres et les espaces topologiques Notas de Lógica Matemática, Vol. 29–30, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca, 1974.

[00013] [14] L. Monteiro: “Algèbre du calcul propositionel trivalent de Heyting”, Fund. Math., Vol. 74, (1972), pp. 99–109.

[00014] [15] L. Monteiro: Algebras de Lukasiewicz trivalentes monádicas, Notas de Logica Matemática, Vol. 32, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca, 1974.

[00015] [16] C.O. Sicoe: “Sur les ideaux des algèbres Lukasiewicziennes polivalentes” Rev. Roum. Math. Pures et Appl., Vol. 12, (1967), pp. 391–401.

[00016] [17] C.O. Sicoe: “On many-valued Lukasiewicz algebra” Proc. Japan Acad., Vol. 43, (1967), pp. 725–728. http://dx.doi.org/10.3792/pja/1195521470