On the lattice of deductive systems of a BL-algebra

Dumitru Bu§neag; Dana Piciu

Open Mathematics (2003)

  • Volume: 1, Issue: 2, page 221-237
  • ISSN: 2391-5455

Abstract

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For a BL-algebra A we denote by Ds(A) the lattice of all deductive systems of A. The aim of this paper is to put in evidence new characterizations for the meet-irreducible elements on Ds(A). Hyperarchimedean BL-algebras, too, are characterized.

How to cite

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Dumitru Bu§neag, and Dana Piciu. "On the lattice of deductive systems of a BL-algebra." Open Mathematics 1.2 (2003): 221-237. <http://eudml.org/doc/268745>.

@article{DumitruBu2003,
abstract = {For a BL-algebra A we denote by Ds(A) the lattice of all deductive systems of A. The aim of this paper is to put in evidence new characterizations for the meet-irreducible elements on Ds(A). Hyperarchimedean BL-algebras, too, are characterized.},
author = {Dumitru Bu§neag, Dana Piciu},
journal = {Open Mathematics},
keywords = {03G10},
language = {eng},
number = {2},
pages = {221-237},
title = {On the lattice of deductive systems of a BL-algebra},
url = {http://eudml.org/doc/268745},
volume = {1},
year = {2003},
}

TY - JOUR
AU - Dumitru Bu§neag
AU - Dana Piciu
TI - On the lattice of deductive systems of a BL-algebra
JO - Open Mathematics
PY - 2003
VL - 1
IS - 2
SP - 221
EP - 237
AB - For a BL-algebra A we denote by Ds(A) the lattice of all deductive systems of A. The aim of this paper is to put in evidence new characterizations for the meet-irreducible elements on Ds(A). Hyperarchimedean BL-algebras, too, are characterized.
LA - eng
KW - 03G10
UR - http://eudml.org/doc/268745
ER -

References

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  1. [1] R. Balbes and Ph. Dwinger: Distributive Lattices, University of Missouri Press, 1974. 
  2. [2] D. Bu§neag and D. Piciu: “Meet-irreducible ideals in an MV-algebra”, Analele Universitąţii din Craiova, Seria Matematica-Informatica, Vol. XXVIII, (2001), pp. 110–119. Zbl1058.06014
  3. [3] D. Buşneag and D. Piciu: “On the lattice of ideals of an MV-algebra”, Scientiae Mathematicae Japonicae, Vol. 56, (2002), pp. 367–372. Zbl1019.06004
  4. [4] R. Cignoli, I.M.L. D'Ottaviano, D. Mundici: Algebraic foundation of many-valued reasoning, Kluwer Academic Publ., Dordrecht, 2000. 
  5. [5] A. Diego: “Sur les algèbres de Hilbert”, In. Ed. Hermann: Collection de Logique Mathématique, Serie A, XXI, Paris, 1966. Zbl0144.00105
  6. [6] G. Grätzer: Lattice theory, W. H. Freeman and Company, San Francisco, 1979. 
  7. [7] G. Georgescu and M. Ploščica: “Values and minimal spectrum of an algebraic lattice”, Math. Slovaca, Vol. 52, (2002), pp. 247–253. Zbl1008.06006
  8. [8] P. Hájek: Metamathematics of Fuzzy Logic, Kluwer Academic Publ., Dordrecht, 1998. 
  9. [9] A. Iorgulescu: “Iséki algebras. Connections with BL-algebras”, to appear in Soft Computing. Zbl1075.06009
  10. [10] A. Di Nola, G. Georgescu, A. Iorgulescu: “Pseudo-BL-algebras”, to appear in Multiple Valued Logic. Zbl1028.06007
  11. [11] H. Rasiowa, An Algebraic Approach to Non-Classical Logics, PWN and North-Holland Publishing Company, 1974. Zbl0299.02069
  12. [12] E. Turunen: Mathematics Behind Fuzzy Logic, Physica-Verlag, 1999. Zbl0940.03029

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