General lattice theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1978
|
| Ausgabe: | 1. Aufl. |
| Schriftenreihe: | Lehrbücher und Monographien auf dem Gebiete der exakten Wissenschaften / Mathematische Reihe
52 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XIII, 381 S. graph. Darst. |
| ISBN: | 3764308133 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804115423198707712 |
|---|---|
| adam_text | CONTENTS
PREFACE AND ACKNOWLEDGEMENTS IX
INTRODUCTION XI
I. FIRST CONCEPTS
1. Two Definitions of Lattices 1
2. How to Describe Lattices 9
3. Some Algebraic Concepts 15
4. Polynomials, Identities, and Inequalities 26
5. Free Lattices 32
6. Special Elements 47
Further Topics and References 52
Problems 56
II. DISTRIBUTIVE LATTICES
1. Characterization Theorems and Representation Theorems 59
2. Polynomials and Freeness 68
3. Congruence Relations 73
4. Boolean Algebras R-generated by Distributive Lattices 86
5. Topological Representation 99
6. Distributive Lattices with Pseudocomplementation Ill
Further Topics and References 120
Problems 126
III. CONGRUENCES AND IDEALS
1. Weak Projectivity and Congruences 129
2. Distributive, Standard, and Neutral Elements 138
3. Distributive, Standard, and Neutral Ideals 146
4. Structure Theorems 151
Further Topics and References 158
Problems 159
IV. MODULAR AND SEMIMODULAR LATTICES
1. Modular Lattices 161
2. Semimodular Lattices 172
3. Geometric Lattices 178
VIII Contents
4. Partition Lattices 192
5. Complemented Modular Lattices 201
Further Topics and References 218
Problems 224
V. EQUATIONAL CLASSES OF LATTICES
1. Characterizations of Equational Classes 227
2. The Lattice of Equational Classes of Lattices 236
3. Finding Equational Bases 243
4. The Amalgamation Property 252
Further Topics and References 260
Problems 262
VI. FREE PRODUCTS
1. Free Products of Lattices 265
2. The Structure of Free Lattices 282
3. Reduced Free Products 288
4. Hopfian Lattices 298
Further Topics and References 303
Problems 306
CONCLUDING REMARKS 311
BIBLIOGRAPHY 316
TABLE OF NOTATION 362
INDEX 365
CONTENTS
PREFACE AND ACKNOWLEDGEMENTS IX
INTRODUCTION XI
I. FIRST CONCEPTS
1. Two Definitions of Lattices 1
2. How to Describe Lattices 9
3. Some Algebraic Concepts 15
4. Polynomials, Identities, and Inequalities 26
5. Free Lattices 32
6. Special Elements 47
Further Topics and References 52
Problems 56
II. DISTRIBUTIVE LATTICES
1. Characterization Theorems and Representation Theorems 59
2. Polynomials and Freeness 68
3. Congruence Relations 73
4. Boolean Algebras R generated by Distributive Lattices 86
5. Topological Representation 99
6. Distributive Lattices with Pseudocomplementation Ill
Further Topics and References 120
Problems 126
III. CONGRUENCES AND IDEALS
1. Weak Projectivity and Congruences 129
2. Distributive, Standard, and Neutral Elements 138
3. Distributive, Standard, and Neutral Ideals 146
4. Structure Theorems 151
Further Topics and References 158
Problems 159
IV. MODULAR AND SEMIMODULAR LATTICES
1. Modular Lattices 161
2. Semimodular Lattices 172
3. Geometric Lattices 178
VIII Contents
4. Partition Lattices 192
5. Complemented Modular Lattices 201
Further Topics and References 218
Problems 224
V. EQUATIONAL CLASSES OF LATTICES
1. Characterizations of Equational Classes 227
2. The Lattice of Equational Classes of Lattices 236
3. Finding Equational Bases 243
4. The Amalgamation Property 252
Further Topics and References 260
Problems 262
VI. FREE PRODUCTS
1. Free Products of Lattices 265
2. The Structure of Free Lattices 282
3. Reduced Free Products 288
4. Hopfian Lattices 298
Further Topics and References 303
Problems 306
CONCLUDING REMARKS 311
BIBLIOGRAPHY 316
TABLE OF NOTATION 362
INDEX 365
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 528 - Ephemerides |
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| discipline | Physik Mathematik |
| edition | 1. Aufl. |
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| id | DE-604.BV001001103 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:22:22Z |
| institution | BVB |
| isbn | 3764308133 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000605632 |
| oclc_num | 299983585 |
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| physical | XIII, 381 S. graph. Darst. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Lehrbücher und Monographien auf dem Gebiete der exakten Wissenschaften / Mathematische Reihe |
| spelling | Grätzer, George 1936- Verfasser (DE-588)10907873X aut General lattice theory 1. Aufl. Basel [u.a.] Birkhäuser 1978 XIII, 381 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lehrbücher und Monographien auf dem Gebiete der exakten Wissenschaften / Mathematische Reihe 52 Partiële orde gtt Treillis, Théorie des Lattice theory Verbandstheorie (DE-588)4127072-1 gnd rswk-swf Verbandstheorie (DE-588)4127072-1 s DE-604 Mathematische Reihe Lehrbücher und Monographien auf dem Gebiete der exakten Wissenschaften 52 (DE-604)BV000003214 52 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000605632&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000605632&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grätzer, George 1936- General lattice theory Partiële orde gtt Treillis, Théorie des Lattice theory Verbandstheorie (DE-588)4127072-1 gnd |
| subject_GND | (DE-588)4127072-1 |
| title | General lattice theory |
| title_auth | General lattice theory |
| title_exact_search | General lattice theory |
| title_full | General lattice theory |
| title_fullStr | General lattice theory |
| title_full_unstemmed | General lattice theory |
| title_short | General lattice theory |
| title_sort | general lattice theory |
| topic | Partiële orde gtt Treillis, Théorie des Lattice theory Verbandstheorie (DE-588)4127072-1 gnd |
| topic_facet | Partiële orde Treillis, Théorie des Lattice theory Verbandstheorie |
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| volume_link | (DE-604)BV000003214 |
| work_keys_str_mv | AT gratzergeorge generallatticetheory |
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