12 papers
Multi-algebras as tolerance quotients of algebras
G. Grätzer, R. Quackenbush
If is an algebra and \bgt is a tolerance on , then $A/\bgt$ is a multi-algebra in a natural way. We give an example to show that not every multi-algebra arises in this manne…
On the algorithmic construction of the 1960 sectional complement
G. Grätzer, G. Klus, A. Nguyen
In 1960, G. Grätzer and E.\,T. Schmidt proved that every finite distributive lattice can be represented as the congruence lattice of a sectionally complemented finite lattice .…
Lattice tolerances and congruences
Gábor Czédli, George Grätzer
We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.
Notes on planar semimodular lattices. VI. On the structure theorem of planar semimodular lattices
G. Grätzer
In a recent paper, G. Czédli and E.\,T. Schmidt present a structure theorem for planar semimodular lattices. In this note, we present an alternative proof.
Homomorphisms and principal congruences of bounded lattices. III. The Independence Theorem
G. Grätzer
A new result of G. Czédli states that for an ordered set with at least two elements and a group , there exists a bounded lattice such that the ordered set of principal c…
Congruence structure of planar semimodular lattices: The General Swing Lemma
Gábor Czédli, George Grätzer, Harry Lakser
The Swing Lemma of the second author describes how a congruence spreads from a prime interval to another in a slim (having no sublattice), planar, semimodular lattice. We gen…