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Variety of doubly Heyting algebras is congruence uniform. (English) Zbl 0666.06008
A congruence on an algebra is said to be uniform if all its congruence classes have the same cardinality and an algebra is called congruence uniform if all its congruences are uniform. In this paper the authors show that every double Heyting algebra is congruence uniform and characterize those that are strongly congruence uniform; by which it is meant that every congruence on it has the property that its congruence classes are isomorphic lattices.
Reviewer: R.Beazer
MSC:
06D20 Heyting algebras (lattice-theoretic aspects)
08B99 Varieties
06B20 Varieties of lattices
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