Notes on monadic n -valued Łukasiewicz algebras

A. V. Figallo; Inés Pascual; Alicia Ziliani

Mathematica Bohemica (2004)

  • Volume: 129, Issue: 3, page 255-271
  • ISSN: 0862-7959

Abstract

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A topological duality for monadic n -valued Łukasiewicz algebras introduced by M. Abad (Abad, M.: Estructuras cíclica y monádica de un álgebra de Łukasiewicz n -valente. Notas de Lógica Matemática 36. Instituto de Matemática. Universidad Nacional del Sur, 1988) is determined. When restricted to the category of Q -distributive lattices and Q -homomorphims, it coincides with the duality obtained by R. Cignoli in 1991. A new characterization of congruences by means of certain closed and involutive subsets of the associated space is also obtained. This allowed us to describe subdirectly irreducible algebras in this variety, arriving by a different method at the results established by Abad.

How to cite

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Figallo, A. V., Pascual, Inés, and Ziliani, Alicia. "Notes on monadic $n$-valued Łukasiewicz algebras." Mathematica Bohemica 129.3 (2004): 255-271. <http://eudml.org/doc/249395>.

@article{Figallo2004,
abstract = {A topological duality for monadic $n$-valued Łukasiewicz algebras introduced by M. Abad (Abad, M.: Estructuras cíclica y monádica de un álgebra de Łukasiewicz $n$-valente. Notas de Lógica Matemática 36. Instituto de Matemática. Universidad Nacional del Sur, 1988) is determined. When restricted to the category of $Q$-distributive lattices and $Q$-homomorphims, it coincides with the duality obtained by R. Cignoli in 1991. A new characterization of congruences by means of certain closed and involutive subsets of the associated space is also obtained. This allowed us to describe subdirectly irreducible algebras in this variety, arriving by a different method at the results established by Abad.},
author = {Figallo, A. V., Pascual, Inés, Ziliani, Alicia},
journal = {Mathematica Bohemica},
keywords = {$n$-valued Łukasiewicz algebras; Priestley spaces; congruences; subdirectly irreducible algebras; -valued Łukasiewicz algebras; Priestley spaces; congruences; subdirectly irreducible algebras},
language = {eng},
number = {3},
pages = {255-271},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Notes on monadic $n$-valued Łukasiewicz algebras},
url = {http://eudml.org/doc/249395},
volume = {129},
year = {2004},
}

TY - JOUR
AU - Figallo, A. V.
AU - Pascual, Inés
AU - Ziliani, Alicia
TI - Notes on monadic $n$-valued Łukasiewicz algebras
JO - Mathematica Bohemica
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 129
IS - 3
SP - 255
EP - 271
AB - A topological duality for monadic $n$-valued Łukasiewicz algebras introduced by M. Abad (Abad, M.: Estructuras cíclica y monádica de un álgebra de Łukasiewicz $n$-valente. Notas de Lógica Matemática 36. Instituto de Matemática. Universidad Nacional del Sur, 1988) is determined. When restricted to the category of $Q$-distributive lattices and $Q$-homomorphims, it coincides with the duality obtained by R. Cignoli in 1991. A new characterization of congruences by means of certain closed and involutive subsets of the associated space is also obtained. This allowed us to describe subdirectly irreducible algebras in this variety, arriving by a different method at the results established by Abad.
LA - eng
KW - $n$-valued Łukasiewicz algebras; Priestley spaces; congruences; subdirectly irreducible algebras; -valued Łukasiewicz algebras; Priestley spaces; congruences; subdirectly irreducible algebras
UR - http://eudml.org/doc/249395
ER -

References

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