Displaying similar documents to “On the variety Csub ( D )

Separation properties in congruence lattices of lattices

Miroslav Ploščica (2000)

Colloquium Mathematicae

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We investigate the congruence lattices of lattices in the varieties n . Our approach is to represent congruences by open sets of suitable topological spaces. We introduce some special separation properties and show that for different n the lattices in n have different congruence lattices.

Finitely generated almost universal varieties of 0 -lattices

Václav Koubek, Jiří Sichler (2005)

Commentationes Mathematicae Universitatis Carolinae

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A concrete category 𝕂 is (algebraically) if any category of algebras has a full embedding into 𝕂 , and 𝕂 is if there is a class 𝒞 of 𝕂 -objects such that all non-constant homomorphisms between them form a universal category. The main result of this paper fully characterizes the finitely generated varieties of 0 -lattices which are almost universal.

Combinatorial trees in Priestley spaces

Richard N. Ball, Aleš Pultr, Jiří Sichler (2005)

Commentationes Mathematicae Universitatis Carolinae

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We show that prohibiting a combinatorial tree in the Priestley duals determines an axiomatizable class of distributive lattices. On the other hand, prohibiting n -crowns with n 3 does not. Given what is known about the diamond, this is another strong indication that this fact characterizes combinatorial trees. We also discuss varieties of 2-Heyting algebras in this context.