Lattices freely generated by partially ordered sets: which can be "drawn"?
Lattices in quasiordered sets
Lattices of compatible relations
Lattices of convex equivalences
Lattices of fuzzy objects.
Lattices of generating systems
Lattices of lower finite breadth.
Lattices of order ideals on ordered semigroups.
Lattices of partially local Fitting classes.
Lattices of quasiorders on universal algebras
Lattices of Scott-closed sets
A dcpo is continuous if and only if the lattice of all Scott-closed subsets of is completely distributive. However, in the case where is a non-continuous dcpo, little is known about the order structure of . In this paper, we study the order-theoretic properties of for general dcpo’s . The main results are: (i) every is C-continuous; (ii) a complete lattice is isomorphic to for a complete semilattice if and only if is weak-stably C-algebraic; (iii) for any two complete semilattices...
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 and right semi-uninorms on a complete lattice
Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary...
Left translations of compact semilattices and generalizations
Length of ideals in lattices.
Lines in directed distributive multilattices
Local polynomial functions on lattices and universal algebras