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.

Preface Author's Note1 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 Modules5 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 SourcesLocation of Numbered ItemsIndex