Lattice theory / by Thomas Donnellan.

Format:

Book

Author/Creator:

Donnellan, Thomas, author.

Series:

Commonwealth and international library. Mathematics division.

Commonwealth and International Library. Mathematics Division

Language:

English

Subjects (All):

Lattice theory.

Physical Description:

1 online resource (297 p.)

Place of Publication:

Oxford, England : Pergamon Press, 1969.

Language Note:

English

Summary:

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 properti

Contents:

Front Cover; Lattice Theory; Copyright Page; Table of Contents; PREFACE; AUTHOR'S NOTE; Chapter 1. Sets and Relations; 1. Sets; 2. The natural numbers; 3. Relations and operations; 4. Equivalence relations; 5. Congruence relations; Chapter 2. Definition of a Lattice; 6. Partial order; 7. Chains; 8. Lattices; 9. Examples of lattices; Chapter 3. Lattices in General; 10. Duality; 11. Meets and joins; 12. Length and covering conditions; 13. Complements; 14. Sublattices; 15. Homomorphisms; Chapter 4. Modular Lattices; 16. Modularity

17. Length and covering conditions 18. Irreducible elements; 19. Complements; 20. Groups and modules; Chapter 5. Semi-modular Lattices; 21. Semi-modularity; 22. Length and covering conditions; 23. Complements and atoms; 24. Partitions; Chapter 6. Distributive Lattices; 25. Distributivity; 26. Irreducible elements; 27. Boolean algebras; 28. Skolem algebras; 29. Logic; LIST OF SOURCES; LOCATION OF NUMBERED ITEMS; INDEX

Notes:

Includes index.

Description based on print version record.

ISBN:

1-4831-4749-5