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Almost ff-universal and q-universal varieties of modular 0-lattices

V. Koubek, J. Sichler (2004)

Colloquium Mathematicae

A variety 𝕍 of algebras of a finite type is almost ff-universal if there is a finiteness-preserving faithful functor F: 𝔾 → 𝕍 from the category 𝔾 of all graphs and their compatible maps such that Fγ is nonconstant for every γ and every nonconstant homomorphism h: FG → FG' has the form h = Fγ for some γ: G → G'. A variety 𝕍 is Q-universal if its lattice of subquasivarieties has the lattice of subquasivarieties of any quasivariety of algebras of a finite type as the quotient of its sublattice....

Embedding sums of cancellative modes into semimodules

Anna B. Romanowska, Anna Zamojska-Dzienio (2005)

Czechoslovak Mathematical Journal

A mode (idempotent and entropic algebra) is a Lallement sum of its cancellative submodes over a normal band if it has a congruence with a normal band quotient and cancellative congruence classes. We show that such a sum embeds as a subreduct into a semimodule over a certain ring, and discuss some consequences of this fact. The result generalizes a similar earlier result of the authors proved in the case when the normal band is a semilattice.

Finite atomistic lattices that can be represented as lattices of quasivarieties

K. Adaricheva, Wiesław Dziobiak, V. Gorbunov (1993)

Fundamenta Mathematicae

We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].

Finitely generated almost universal varieties of 0 -lattices

Václav Koubek, Jiří Sichler (2005)

Commentationes Mathematicae Universitatis Carolinae

A concrete category 𝕂 is (algebraically) universal if any category of algebras has a full embedding into 𝕂 , and 𝕂 is almost universal 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.

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...

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