4 papers
Homomorphisms of distributive lattices as restrictions of congruences. III. Rectangular lattices and two convex sublattices
George Grätzer, Harry Lakser
Let be a finite lattice and let be an ideal of . Then the restriction map is a bounded lattice homomorphism of the congruence lattice of~ into the congruence lattice…
Minimal representations of a finite distributive lattice by principal congruences of a lattice
G. Grätzer, H. Lakser
Let the finite distributive lattice be isomorphic to the congruence lattice of a finite lattice . Let denote those elements of that correspond to principal congruenc…
Revisiting the representation theorem of finite distributive lattices with principal congruences
G. Grätzer, H. Lakser
A classical result of R.\,P. Dilworth states that every finite distributive lattice can be represented as the congruence lattice of a finite lattice~. A~sharper form was pub…
Some preliminary results on the set of principal congruences of a finite lattice
G. Grätzer, H. Lakser
In the second edition of the congruence lattice book, Problem 22.1 asks for a characterization of subsets of a finite distributive lattice such that there is a finite latti…