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Aldo V. Figallo, Departamento de Matematica, Universidad Nacional del Sur, 8000 Bahia Blanca, Argentina; Instituto de Ciencias Basicas. Universidad Nacional de San Juan, 5400 San Juan, Argentina, e-mail: matfiga@criba.edu.ar. Ines B. Pascual, Instituto de Ciencias Basicas, Universidad Nacional de San Juan, 5400 San Juan, Argentina, e-mail: ipascual@ffha.unsj.edu.ar. Alicia N. Ziliani, Departamento de Matematica, Universidad Nacional del Sur, 8000 Bahia Blanca, Argentina; Instituto de Ciencias Basicas, Universidad Nacional de San Juan, 5400 San Juan, Argentina, e-mail: aziliani@criba.edu.ar
Abstract: A topological duality for monadic $n$-valued Lukasiewicz algebras introduced by M. Abad (Abad, M.: Estructuras ciclica y monadica de un algebra de Lukasiewicz $n$-valente. Notas de Logica Matematica 36. Instituto de Matematica. 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.
Keywords: $n$-valued Lukasiewicz algebras, Priestley spaces, congruences, subdirectly irreducible algebras
Classification (MSC 2000): 06D30, 03G20
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