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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.

MSC:
06D05 Structure and representation theory of distributive lattices
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