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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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Basel :
Springer Basel : Imprint: Birkhäuser,
2011.
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| Edición: | 1st ed. 2011. |
| Temas: | |
| Acceso en línea: | Texto Completo |
Tabla de Contenidos:
- 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.