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Notes on monadic $$n$$-valued Łukasiewicz algebras. (English) Zbl 1080.06011
Summary: A topological duality for monadic $$n$$-valued Łukasiewicz algebras introduced by M. Abad [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 allows us to describe subdirectly irreducible algebras in this variety, arriving by a different method at the results established by Abad.

##### MSC:
 06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects) 03G20 Logical aspects of Łukasiewicz and Post algebras
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