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Lattice Theory - 1st Edition - ISBN: 9780080125633, 9781483147499

Lattice Theory

1st Edition

The Common Wealth and International Library: Mathematics Division

Author: Thomas Donnellan
Editors: W. J. Langford E. A. Maxwell C. Plumpton
eBook ISBN: 9781483147499
Imprint: Pergamon
Published Date: 1st January 1968
Page Count: 296
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Lattice Theory presents an elementary account of a significant branch of contemporary mathematics concerning lattice theory. This book discusses the unusual features, which include the presentation and exploitation of partitions of a finite set. Organized into six chapters, this book begins with an overview of the concept of several topics, including sets in general, the relations and operations, the relation of equivalence, and the relation of congruence. This text then defines the relation of partial order and then partially ordered sets, including chains. Other chapters examine the properties of meet and join and explain dimensional considerations. This book discusses as well certain relations between individual elements of a lattice, between subsets of a lattice, and between lattices themselves. The final chapter deals with distributive lattices and explores the complements in distributive lattices. This book is a valuable resource for college and university students of mathematics, logic, and such technologies as communications engineering.

Table of Contents


Author's Note

1 Sets and Relations

§ 1 Sets

§ 2 The Natural Numbers

§ 3 Relations and Operations

§ 4 Equivalence Relations

§ 5 Congruence Relations

2 Definition of a Lattice

§ 6 Partial Order

§ 7 Chains

§ 8 Lattices

§ 9 Examples of Lattices

(1) Small Finite Lattices

(2) Boolean Lattices

(3) Factorization Lattices

(4) Equivalence or Partition Lattices

(5) Chains

(6) Cardinal Products

3 Lattices in General

§ 10 Duality

§ 11 Meets and Joins

§ 12 Length and Covering Conditions

§ 13 Complements

§ 14 Sublattices

§ 15 Homomorphisms

4 Modular Lattices

§ 16 Modularity

§ 17 Length and Covering Conditions

§ 18 Irreducible Elements

§ 19 Complements

§ 20 Groups and Modules

5 Semi-modular Lattices

§ 21 Semi-Modularity

§ 22 Length and Covering Conditions

§ 23 Complements and Atoms


6 Distributive Lattices

§ 25 Distributivity

§ 26 Irreducible elements

§ 27 Boolean Algebras

(1) Complements

(2) Atoms

(3) Subalgebras

(4) Ideals

§ 28 Skolem Algebras

§ 29 Logic

List of Sources

Location of Numbered Items



No. of pages:
© Pergamon 1968
1st January 1968
eBook ISBN:

About the Author

Thomas Donnellan

About the Editors

W. J. Langford

E. A. Maxwell

C. Plumpton

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