Simple and subdirectly irreducibles bounded distributive lattices with unary operators.

*(English)*Zbl 1130.06005Summary: 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 |

##### Keywords:

subdirectly irreducible algebras; varieties of distributive lattices with unary operators; modal algebras; varieties of Heyting algebras with operators
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\textit{S. A. Celani}, Int. J. Math. Math. Sci. 2006, No. 15, Article ID 21835, 20 p. (2006; Zbl 1130.06005)

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