Geodesic
Notes on monadic $n$-valued Łukasiewicz algebras
Mathematica Bohemica, Tome 129 (2004) no. 3, pp. 255-271

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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.
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.
DOI : 10.21136/MB.2004.134149
Classification : 03G20, 06D30, 06D50
Keywords: $n$-valued Łukasiewicz algebras; Priestley spaces; congruences; subdirectly irreducible algebras 
Figallo, A. V.; Pascual, I.; Ziliani, A. Notes on monadic $n$-valued Łukasiewicz algebras. Mathematica Bohemica, Tome 129 (2004) no. 3, pp. 255-271. doi: 10.21136/MB.2004.134149
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