Notes on monadic $n$-valued Łukasiewicz algebras
2004; Institute of Mathematics of the Czech Academy of Sciences; Volume: 129; Issue: 3 Linguagem: Inglês
10.21136/mb.2004.134149
ISSN2464-7136
AutoresAldo V. Figallo, Inés Pascual, Alicia Ziliani,
Tópico(s)Fuzzy and Soft Set Theory
ResumoA 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.
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