E-Book, Englisch, 296 Seiten, Web PDF
Donnellan / Langford / Maxwell Lattice Theory
1. Auflage 2014
ISBN: 978-1-4831-4749-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
The Common Wealth and International Library: Mathematics Division
E-Book, Englisch, 296 Seiten, Web PDF
ISBN: 978-1-4831-4749-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Lattice Theory;4
3;Copyright Page;5
4;Table of Contents;8
5;PREFACE;10
6;AUTHOR'S NOTE;12
7;Chapter 1. Sets and Relations;14
7.1;§ 1. Sets;14
7.2;§ 2. The natural numbers;16
7.3;§ 3. Relations and operations;21
7.4;§ 4. Equivalence relations;26
7.5;§ 5. Congruence relations;35
8;Chapter 2. Definition of a Lattice;43
8.1;§ 6. Partial order;43
8.2;§ 7. Chains;51
8.3;§ 8. Lattices;56
8.4;§ 9. Examples of lattices;66
9;Chapter 3. Lattices in General;88
9.1;§ 10. Duality;88
9.2;§ 11. Meets and joins;90
9.3;§ 12. Length and covering conditions;98
9.4;§ 13. Complements;114
9.5;§ 14. Sublattices;117
9.6;§ 15. Homomorphisms;130
10;Chapter 4. Modular Lattices;147
10.1;§ 16. Modularity;147
10.2;§ 17. Length and covering conditions;157
10.3;§ 18. Irreducible elements;161
10.4;§ 19. Complements;172
10.5;§ 20. Groups and modules;178
11;Chapter 5. Semi-modular Lattices;190
11.1;§ 21. Semi-modularity;190
11.2;§ 22. Length and covering conditions;202
11.3;§ 23. Complements and atoms;206
11.4;§ 24. Partitions;210
12;Chapter 6. Distributive Lattices;215
12.1;§ 25. Distributivity;215
12.2;§ 26. Irreducible elements;225
12.3;§ 27. Boolean algebras;237
12.4;§ 28. Skolem algebras;262
12.5;§ 29. Logic;277
13;LIST OF SOURCES;291
14;LOCATION OF NUMBERED ITEMS;292
15;INDEX;294
