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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...

Lattice-theoretically characterized classes of finite bands

Reinhard Thron, Jörg Koppitz (2003)

Archivum Mathematicum

There are investigated classes of finite bands such that their subsemigroup lattices satisfy certain lattice-theoretical properties which are related with the cardinalities of the Green’s classes of the considered bands, too. Mainly, there are given disjunctions of equations which define the classes of finite bands.

Linear identities in graph algebras

Agata Pilitowska (2009)

Commentationes Mathematicae Universitatis Carolinae

We find the basis of all linear identities which are true in the variety of entropic graph algebras. We apply it to describe the lattice of all subvarieties of power entropic graph algebras.

Locally finite M-solid varieties of semigroups

Klaus Denecke, Bundit Pibaljommee (2003)

Discussiones Mathematicae - General Algebra and Applications

An algebra of type τ is said to be locally finite if all its finitely generated subalgebras are finite. A class K of algebras of type τ is called locally finite if all its elements are locally finite. It is well-known (see [2]) that a variety of algebras of the same type τ is locally finite iff all its finitely generated free algebras are finite. A variety V is finitely based if it admits a finite basis of identities, i.e. if there is a finite set σ of identities such that V = ModΣ, the class of...

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