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In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.
In this paper, the variety of closure n-valued Łukasiewicz algebras, that is, Łukasiewicz algebras of order n endowed with a closure operator, is investigated. The lattice of subvarieties in the particular case in which the open elements form a three-valued Heyting algebra is obtained.
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