Skip to main content
Elsevier

Lattice Theory

The Common Wealth and International Library: Mathematics Division

  • 1st Edition - January 1, 1968
  • Latest edition
  • Author: Thomas Donnellan
  • Editors: W. J. Langford, E. A. Maxwell, C. Plumpton
  • Language: English

Lattice Theory presents an elementary account of a significant branch of contemporary mathematics concerning lattice theory. This book discusses the unusual features, which include… Read more

Data Mining & ML

Unlock the cutting edge

Up to 20% on trusted resources. Build expertise with data mining, ML methods.

Explore now

Description

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


Preface

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

Partitions


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

Index


Product details

  • Edition: 1
  • Latest edition
  • Published: September 13, 2014
  • Language: English

View book on ScienceDirect

Read Lattice Theory on ScienceDirect