Lattice betweenness relation and a generalization of König's lemma
Lattices and semilattices having an antitone involution in every upper interval
We study -semilattices and lattices with the greatest element 1 where every interval [p,1] is a lattice with an antitone involution. We characterize these semilattices by means of an induced binary operation, the so called sectionally antitone involution. This characterization is done by means of identities, thus the classes of these semilattices or lattices form varieties. The congruence properties of these varieties are investigated.
Lattices in quasiordered sets
Lattices of compatible relations
Lattices of generating systems
Lattices of lower finite breadth.
Lattices of tolerances
Lattices with a third distributive operation
Lattices with complemented tolerance lattice
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
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.
Left translations of compact semilattices and generalizations
Lines in directed distributive multilattices