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Title: Notes on monadic $n$-valued Łukasiewicz algebras (English)
Author: Figallo, A. V.
Author: Pascual, I.
Author: Ziliani, A.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 129
Issue: 3
Year: 2004
Pages: 255-271
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: $n$-valued Łukasiewicz algebras
Keyword: Priestley spaces
Keyword: congruences
Keyword: subdirectly irreducible algebras
MSC: 03G20
MSC: 06D30
MSC: 06D50
idZBL: Zbl 1080.06011
idMR: MR2092712
DOI: 10.21136/MB.2004.134149
Date available: 2009-09-24T22:14:50Z
Last updated: 2020-07-29
Stable URL:
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