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Bounded distributive lattice expansions. (English) Zbl 1077.06008
A new notion of a canonical extension algebra \(A=(A_0, \omega^A,\omega\in\Omega)\) (consisting of a bounded distributive lattice \(A_0\) with completely arbitrary auxiliary operations) is introduced in the paper. The notion is a generalization of the extension of bounded distributive lattices and it coincides with the earlier ones whenever they apply. A new feature is the introduction of several topologies on the universe of the canonical extensions of a distributive bounded lattices. The definition of the new notion of a canonical extension introduced in the paper makes the concept available for the study of many classes of algebras that did not fall within the scope of the earlier definitions.

06D05 Structure and representation theory of distributive lattices
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