Closure Łukasiewicz algebras

Abad Manuel; Cimadamore Cecilia; Díaz Varela José; Rueda Laura; Suardíaz Ana

Open Mathematics (2005)

  • Volume: 3, Issue: 2, page 215-227
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Abad Manuel, et al. "Closure Łukasiewicz algebras." Open Mathematics 3.2 (2005): 215-227. <http://eudml.org/doc/268692>.

@article{AbadManuel2005,
abstract = {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.},
author = {Abad Manuel, Cimadamore Cecilia, Díaz Varela José, Rueda Laura, Suardíaz Ana},
journal = {Open Mathematics},
keywords = {06D30; 03G20; 08B15},
language = {eng},
number = {2},
pages = {215-227},
title = {Closure Łukasiewicz algebras},
url = {http://eudml.org/doc/268692},
volume = {3},
year = {2005},
}

TY - JOUR
AU - Abad Manuel
AU - Cimadamore Cecilia
AU - Díaz Varela José
AU - Rueda Laura
AU - Suardíaz Ana
TI - Closure Łukasiewicz algebras
JO - Open Mathematics
PY - 2005
VL - 3
IS - 2
SP - 215
EP - 227
AB - 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.
LA - eng
KW - 06D30; 03G20; 08B15
UR - http://eudml.org/doc/268692
ER -

References

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  1. [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.  
  2. [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 
  3. [3] R. Balbes and P. Dwinger: Distributive Lattices, University of Missouri Press, Columbia, MO, 1974.  
  4. [4] G. Bezhanishvili: “Locally finite varieties”, Algebra Universais 46, Vol. 4, 2001, pp. 531–548. http://dx.doi.org/10.1007/PL00000358 
  5. [5] W. Blok: Varieties of interior algebras, Thesis (Ph.D.), University of Amsterdam, 1976.  
  6. [6] V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu: Lukasiewicz-Moisil Algebras, North Holland, 1991.  
  7. [7] R. Cignoli: Moisil Algebras, Notas de Lógica Matemática, Vol. 27, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca, 1970.  
  8. [8] B.A. Davey: “On the lattice of subvarieties”, Houston J. Math., Vol. 5, (1979), pp. 183–192.  
  9. [9] J.P. Díaz Varela: Algebras de Clausura y su Estructura Simétrica, Tesis (Ph.D.), Bahía Blanca, Argentina, 1997.  
  10. [10] L. Iturrioz: “Łukasiewicz and Symmetrical Heyting Algebras”, ZML, Vol. 23(2), (1977), pp. 131–136.  
  11. [11] L. Iturrioz: “Two characteristic properties of three-valued Lukasiewicz algebras” Rep. Math. Logic, Vol. 8, (1977), pp. 63–69.  
  12. [12] Gr.C. Moisil: “Notes sur les logiques non-chrysippiennes”, Ann. Sci. Univ. Jassy, Vol. 27, (1941), pp. 86–98.  
  13. [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.  
  14. [14] L. Monteiro: “Algèbre du calcul propositionel trivalent de Heyting”, Fund. Math., Vol. 74, (1972), pp. 99–109.  
  15. [15] L. Monteiro: Algebras de Lukasiewicz trivalentes monádicas, Notas de Logica Matemática, Vol. 32, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca, 1974.  
  16. [16] C.O. Sicoe: “Sur les ideaux des algèbres Lukasiewicziennes polivalentes” Rev. Roum. Math. Pures et Appl., Vol. 12, (1967), pp. 391–401.  
  17. [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 

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