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Completion and amalgamation of bounded distributive quasi lattices. (English) Zbl 1221.06015

The concept of a quasilattice was introduced by I. Chajda in [“Lattices in quasiordered sets”, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 105, Math. 31, 6–12 (1992; Zbl 0773.06002)], where the basic concepts and properties are shown. The authors present a series of nice results concerning bounded distributive quasilattices. They show that every such quasilattice \(A\) can be represented as a quasilattice of certain mappings from \(A\) into a three-element quasilattice. For this, they use a modification of Priestley duality. They prove that the variety of bounded distributive quasilattices has the amalgamation property and the congruence extension property.

MSC:

06D75 Other generalizations of distributive lattices
06B20 Varieties of lattices

Citations:

Zbl 0773.06002
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