Lattice tolerances and congruences
G\'abor Cz\'edli, George Gr\"atzer
TL;DR
This paper proves that every tolerance relation in a lattice can be represented as a homomorphic image of a congruence relation, providing a new understanding of the structure of lattice relations.
Contribution
It establishes a fundamental link between tolerances and congruences in lattices, showing that tolerances are homomorphic images of congruences.
Findings
Tolerance relations are homomorphic images of congruences in lattices
Provides a structural characterization of tolerances in lattice theory
Enhances understanding of lattice relation representations
Abstract
We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.
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Taxonomy
TopicsAdvanced Algebra and Logic