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Lattices of relative colour-families and antivarieties

Aleksandr Kravchenko — 2007

Discussiones Mathematicae - General Algebra and Applications

We consider general properties of lattices of relative colour-families and antivarieties. Several results generalise the corresponding assertions about colour-families of undirected loopless graphs, see [1]. Conditions are indicated under which relative colour-families form a lattice. We prove that such a lattice is distributive. In the class of lattices of antivarieties of relation structures of finite signature, we distinguish the most complicated (universal) objects. Meet decompositions in lattices...

On the lattices of quasivarieties of differential groupoids

Aleksandr Kravchenko — 2008

Commentationes Mathematicae Universitatis Carolinae

The main result of Romanowska A., Roszkowska B., , Demonstratio Math. (1987), no. 1–2, 277–290, provides us with an explicit description of the lattice of varieties of differential groupoids. In the present article, we show that this variety is 𝒬 -universal, which means that there is no convenient explicit description for the lattice of quasivarieties of differential groupoids. We also find an example of a subvariety of differential groupoids with a finite number of subquasivarieties.

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