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Lattices with complemented tolerance lattice

Sándor Radelecki, Dietmar Schweigert (2004)

Czechoslovak Mathematical Journal

We characterize lattices with a complemented tolerance lattice. As an application of our results we give a characterization of bounded weakly atomic modular lattices with a Boolean tolerance lattice.

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.

Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice

Ivan Chajda, Helmut Länger (2008)

Discussiones Mathematicae - General Algebra and Applications

Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.

Minimal reducible bounds for hom-properties of graphs

Amelie Berger, Izak Broere (1999)

Discussiones Mathematicae Graph Theory

Let H be a fixed finite graph and let → H be a hom-property, i.e. the set of all graphs admitting a homomorphism into H. We extend the definition of → H to include certain infinite graphs H and then describe the minimal reducible bounds for → H in the lattice of additive hereditary properties and in the lattice of hereditary properties.

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