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Simple and subdirectly irreducibles bounded distributive lattices with unary operators. (English) Zbl 1130.06005
Summary: We characterize the simple and subdirectly irreducible distributive algebras in some varieties of distributive lattices with unary operators, including topological and monadic positive modal algebras. Finally, for some varieties of Heyting algebras with operators we apply these results to determine the simple and subdirectly irreducible algebras.

MSC:
06D05 Structure and representation theory of distributive lattices
06B20 Varieties of lattices
06D20 Heyting algebras (lattice-theoretic aspects)
08B26 Subdirect products and subdirect irreducibility
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