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