Congruences on near-Heyting algebras |
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Authors: | Luciano J. González Marina B. Lattanzi |
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Affiliation: | 1.Universidad Nacional de La Pampa. Facultad de Ciencias Exactas y Naturales,Santa Rosa,Argentina |
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Abstract: | A near-Heyting algebra is a join-semilattice with a top element such that every principal upset is a Heyting algebra. We establish a one-to-one correspondence between the lattices of filters and congruences of a near-Heyting algebra. To attain this aim, we first show an embedding from the lattice of filters to the lattice of congruences of a distributive nearlattice. Then, we describe the subdirectly irreducible and simple near-Heyting algebras. Finally, we fully characterize the principal congruences of distributive nearlattices and near-Heyting algebras. We conclude that the varieties of distributive nearlattices and near-Heyting algebras have equationally definable principal congruences. |
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