The congruences of a lattice form the congruence lattice. In the past half-century, the study of congruence lattices has become a large and important field with a great number of interesting and deep results and many open problems. This self-contained exposition by one of the leading experts in lattice theory, George Grätzer, presents the major results on congruence lattices of finite lattices featuring the author's signature "Proof-by-Picture" method and its conversion to transparencies.

Key features:

• Includes the latest findings from a pioneering researcher in the field

• Insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions

• Contains complete proofs, an extensive bibliography and index, and nearly 80 open problems

• Additional information provided by the author online at:

http://www.maths.umanitoba.ca/homepages/gratzer.html/

The book is appropriate for a one-semester graduate course in lattice theory, yet is also designed as a practical reference for researchers studying lattices.

Klappentext

Self-contained exposition presents the major results on congruence lattices of finite lattices

Includes the latest findings from a pioneering researcher in the field

Features the author's signature "Proof-by-Picture" method and its conversion to transparencies

Contains complete proofs, an extensive bibliography and index, and nearly 80 open problems

Excellent grad text and reference

Inhalt

• Table of Notation * Picture Gallery * Preface and Acknowledgment * Introduction Part I: A Brief Introduction to Lattices * Basic Concepts * Special Concepts * Congruences Part II: Basic Techniques * Chopped Lattices * Boolean Triples * Cubic Extensions Part III: Representation Theorems * The Dilworth Theorem * Minimal Representations * Semimodular Lattices * Modular Lattices * Uniform Lattices Part IV: Extensions * Sectionally Complemented Lattices * Semimodular Lattices * Isoform Lattices * Independence Theorems * Magic Wands Part V: Two Lattices * Sublattices * Ideals * Tensor Extensions * Bibliography * Index