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Principal congruences of pseudocomplemented DeMorgan algebras. (English) Zbl 0624.06016

The first result shows that every principal congruence on a de Morgan algebra is the join of two principal lattice congruences. This has previously been known only in the distributive case. The author proceeds to prove that every principal congruence on a pseudo-complemented de Morgan algebra (PCDM) is a countable join of principal lattice congruences. This implies that the variety of distributive PCDMs has the congruence extension property. The remainder of the article investigates certain subvarieties of PCDM and their equational bases.
Reviewer: I.Düntsch

MSC:

06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
06B10 Lattice ideals, congruence relations
06B20 Varieties of lattices
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