The Congruences of a Finite Lattice: A Proof-by-Picture Approach (Hardcover)
The Congruences of a Finite Lattice: A Proof-by-Picture Approach (Hardcover)
Condition
GOOD: This book would have been considered LIKE NEW if it weren't for the defect in the upper left corner of the front cover (seen in the book's image). The binding is tight, the pages are free from writing, and the cover corners are straight. The pages are printed on acid-free paper.
Product Details
From the back cover: "The congruences of a lattice form the congruence lattice. In the past half-century [relative to 2006], 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, and extensive bibliography and index, and nearly 80 open problems...
"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."
BRIEF CONTENTS
I - A Brief Introduction to Lattices
- Basic Concepts
- Special Concepts
- Congruences
II - Basic Techniques
- Chopped Lattices
- Boolean Triples
- Cubic Extensions
III - Representation Theorems
- The Dilworth Theorem
- Minimal Representations
- Semimodular Lattices
- Modular Lattices
- Uniform Lattices
IV - Extensions
- Sectionally Complemented Lattices
- Semimodular Lattices
- Isoform Lattices
- Independence Theorems
- Magic Wands
V - Two Lattices
- Sublattices
- Ideals
- Tensor Extensions
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PUBLISHER: Birkhäuser
ISBN-13: 9780817632243
ISBN-10: 0817632247