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Semi-De Morgan algebras. (English) Zbl 0854.06010
The authors develop a duality for semi-De Morgan algebras built on the Priestley duality for distributive lattices. They characterize the subdirectly irreducible semi-De Morgan algebras, and develop a theory of “partial diagrams” where properties of algebras are tied to the omission of certain partial diagrams from their duals. They use this theory to give axioms for the largest variety of semi-De Morgan algebras with the congruence extension property.

MSC:
06D15 Pseudocomplemented lattices
06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
08B26 Subdirect products and subdirect irreducibility
06B20 Varieties of lattices
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