Lattice Theory: First Concepts and Distributive Lattices

Lattice Theory: First Concepts and Distributive Lattices

by George Gratzer

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Overview


Lattice theory extends into virtually every area of mathematics and offers an ideal framework for understanding basic concepts. This outstanding text is written in clear, direct language and enhanced with many research problems, exercises, diagrams, and concise proofs. The author discusses historical developments as well as future directions and provides extensive end-of-chapter materials and references.
Both novices and experts will benefit from this treatment, which combines the techniques of an introductory text with those of a monograph. It begins with a concise development of the fundamentals of lattice theory and a detailed exploration of free lattices. The core of the text focuses upon the theory of distributive lattices. Diagrams constitute an integral part of the book, along with 500 exercises and 67 original research problems. Eight appendixes, contributed by a group of experts, complement this accessible and informative text.

Product Details

ISBN-13: 9780486471730
Publisher: Dover Publications
Publication date: 03/26/2009
Series: Dover Books on Mathematics Series
Pages: 240
Sales rank: 849,014
Product dimensions: 5.20(w) x 8.10(h) x 0.60(d)

Table of Contents


PREFACE
ACKNOWLEDGMENTS
TABLE OF NOTATION
FIRST CONCEPTS
Two Definitions of Lattices
How to Describe Lattices
Some Algebraic Concepts
Polynomials, Identities, and Inequalities
Free Lattices
Special Elements
Further Topics and References
Problems
DISTRIBUTIVE LATTICES
Characterization Theorems and Representation Theorems
Polynomials and Freeness
Congruence Relations
Boolean Algebras R-generated by Distributive Lattices
Topological Representation
Free Distributive Product
Some Categorical Concepts
Further Topics and References
Problems
DISTRIBUTIVE LATTICES WITH PSEUDOCOMPLEMENTATION
Introduction and Stone Algebras
Identities and Congruences
Representation Theorems
Injective and Free Stone Algebras
Further Topics and References
Problems
BIBLIOGRAPHY
INDEX

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