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ISBN: 9783034800174

This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication … Mehr…

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ISBN: 9783034800174

This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication … Mehr…

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Lattice Theory: Foundation - Erstausgabe

2011

ISBN: 9783034800174

Taschenbuch

[ED: Kartoniert / Broschiert], [PU: Springer Basel], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Authoritative introduction to lattice… Mehr…

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Lattice Theory: Foundation - neues Buch

ISBN: 9783034800174

Based on three previous publications on the subject, this updated third edition covers the key concepts and results in the field. The main topics are distributivity, congruences, construc… Mehr…

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Lattice Theory: Foundation - Taschenbuch

2011, ISBN: 9783034800174

Buch, Softcover, 2011, [PU: Springer Basel], Springer Basel, 2011

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Lattice Theory: Foundation

This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication of the first edition in 1978, General Lattice Theory has become the authoritative introduction to lattice theory for graduate students and the standard reference for researchers. The First Edition set out to introduce and survey lattice theory. Some 12,000 papers have been published in the field since then; so Lattice Theory: Foundation focuses on introducing the field, laying the foundation for special topics and applications. Lattice Theory: Foundation, based on the previous three books, covers the fundamental concepts and results. The main topics are distributivity, congruences, constructions, modularity and semimodularity, varieties, and free products. The chapter on constructions is new, all the other chapters are revised and expanded versions from the earlier volumes. Almost 40 "diamond sections'', many written by leading specialists in these fields, provide a brief glimpse into special topics beyond the basics. "Lattice theory has come a long way... For those who appreciate lattice theory, or who are curious about its techniques and intriguing internal problems, Professor Grätzer's lucid new book provides a most valuable guide to many recent developments. Even a cursory reading should provide those few who may still believe that lattice theory is superficial or naive, with convincing evidence of its technical depth and sophistication." Bulletin of the American Mathematical Society "Grätzer's book General Lattice Theory has become the lattice theorist's bible." Mathematical Reviews

Detailangaben zum Buch - Lattice Theory: Foundation


EAN (ISBN-13): 9783034800174
ISBN (ISBN-10): 3034800177
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2011
Herausgeber: Springer Basel
613 Seiten
Gewicht: 1,024 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2011-04-21T23:22:36+02:00 (Vienna)
Detailseite zuletzt geändert am 2021-11-18T18:12:43+01:00 (Vienna)
ISBN/EAN: 9783034800174

ISBN - alternative Schreibweisen:
3-0348-0017-7, 978-3-0348-0017-4


Daten vom Verlag:

Autor/in: George Grätzer
Titel: Lattice Theory: Foundation
Verlag: Birkhäuser; Springer Basel
614 Seiten
Erscheinungsjahr: 2011-02-07
Basel; CH
Gedruckt / Hergestellt in Niederlande.
Gewicht: 1,213 kg
Sprache: Englisch
85,59 € (DE)
87,99 € (AT)
94,50 CHF (CH)
POD

BC; Book; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Zahlentheorie; Verstehen; lattice theory; universal algebra; B; Number Theory; Number Theory; Mathematics and Statistics; EA

Preface.- Introduction.- Glossary of Notation.- I First Concepts.- 1 Two Definitions of Lattices.- 2 How to Describe Lattices.- 3 Some Basic Concepts.- 4 Terms, Identities, and Inequalities.- 5 Free Lattices.- 6 Special Elements.- II Distributive Lattices.- 1 Characterization and Representation Theorems.- 2 Terms and Freeness.- 3 Congruence Relations.- 4 Boolean Algebras.- 5 Topological Representation.- 6 Pseudocomplementation.- III Congruences.- 1 Congruence Spreading.- 2 Distributive, Standard, and Neutral Elements.- 3 Distributive, Standard, and Neutral Ideals.- 4 Structure Theorems.- IV Lattice Constructions.- 1 Adding an Element.- 2 Gluing.- 3 Chopped Lattices.- 4 Constructing Lattices with Given Congruence Lattices.- 5 Boolean Triples.- V Modular and Semimodular Lattices.- 1 Modular Lattices.- 2 Semimodular Lattices.- 3 Geometric Lattices.- 4 Partition Lattices.- 5 Complemented Modular Lattices.- VI Varieties of Lattices.- 1 Characterizations of Varieties 397.- 2 The Lattice of Varieties of Lattices.- 3 Finding Equational Bases.- 4 The Amalgamation Property.- VII Free Products.- 1 Free Products of Lattices.- 2 The Structure of Free Lattices.- 3 Reduced Free Products.- 4 Hopfian Lattices.- Afterword.- Bibliography.

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