The Congruences of a Finite Lattice: A "Proof-by-Picture" Approach

by George Grätzer

A Brief Introduction to Lattices.- Basic Concepts.- Special Concepts.- Congruences.- Planar Semimodular Lattices.- Some Special Techniques.- Chopped Lattices.- Boolean Triples.- Cubic Extensions.- Congruence Lattices of Finite Lattices.- The Dilworth Theorem.- Minimal Representations.- Semimodular Lattices.- Rectangular Lattices.- Modular Lattices.- Uniform Lattices.- Congruence Lattices and Lattice Extensions.- Sectionally Complemented Lattices.- Semimodular Lattices.- Isoform Lattices.- The Congruence Lattice and the Automorphism Group.- Magic Wands.- Congruence Lattices of Two Related Lattices.- Sublattices.- Ideals.- Tensor Extensions.- VI The Ordered Set of Principal Congruences.- Representation Theorems.- Isotone Maps.- Congruence Structure.- Prime Intervals and Congruences.- Some Applications of the Swing Lemma.

382 pages, Paperback

First published November 9, 2005