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Birkhäuser - Birkhäuser Mathematics | The Congruences of a Finite Lattice - A Proof-by-Picture Approach

The Congruences of a Finite Lattice

A Proof-by-Picture Approach

Grätzer, George

2006, XXVI, 282 p. With online files/update.

A product of Birkhäuser Basel
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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:


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.

Content Level » Research

Keywords » Excel - Lattice - addition - ksa - proof

Related subjects » Birkhäuser Applied Probability and Statistics - Birkhäuser Mathematics

Table of contents 

* 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

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