Lattice Theory: First Concepts and Distributive Lattices - Brossura

Gratzer, George

Brossura

ISBN 10: 048647173X ISBN 13: 9780486471730

Casa editrice: Dover Pubns, 2009

Riassunto

Lattice theory extends into virtually every area of mathematics and offers an ideal framework for understanding basic concepts. This outstanding text is written in clear, direct language and enhanced with many research problems, exercises, diagrams, and concise proofs. The author discusses historical developments as well as future directions and provides extensive end-of-chapter materials and references.
Both novices and experts will benefit from this treatment, which combines the techniques of an introductory text with those of a monograph. It begins with a concise development of the fundamentals of lattice theory and a detailed exploration of free lattices. The core of the text focuses upon the theory of distributive lattices. Diagrams constitute an integral part of the book, along with 500 exercises and 67 original research problems. Eight appendixes, contributed by a group of experts, complement this accessible and informative text.

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Contenuti

PREFACE ACKNOWLEDGMENTS TABLE OF NOTATION FIRST CONCEPTS Two Definitions of Lattices How to Describe Lattices Some Algebraic Concepts Polynomials, Identities, and Inequalities Free Lattices Special Elements Further Topics and References Problems DISTRIBUTIVE LATTICES Characterization Theorems and Representation Theorems Polynomials and Freeness Congruence Relations Boolean Algebras R-generated by Distributive Lattices Topological Representation Free Distributive Product Some Categorical Concepts Further Topics and References Problems DISTRIBUTIVE LATTICES WITH PSEUDOCOMPLEMENTATION Introduction and Stone Algebras Identities and Congruences Representation Theorems Injective and Free Stone Algebras Further Topics and References Problems BIBLIOGRAPHY INDEX

Product Description

Lattice theory offers an ideal framework for understanding basic mathematical concepts. This outstanding text is written in clear, direct language and enhanced with many research problems, exercises, diagrams, and concise proofs. The author discusses historical developments as well as future directions and provides extensive end-of-chapter materials and references. 1971 edition.

Dettagli dell?edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2009
• Lingua: Inglese
• ISBN 10: 048647173X
• ISBN 13: 9780486471730
• Rilegatura: Copertina flessibile
• Numero di pagine: 212
• Contatto del produttore: non disponibile