Universal algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Reidel
1981
|
| Ausgabe: | Rev. ed. |
| Schriftenreihe: | Mathematics and its applications
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 412 S. graph. Darst. |
| ISBN: | 9027712549 9027712131 |
Internformat
MARC
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| 100 | 1 | |a Cohn, Paul M. |d 1924-2006 |e Verfasser |0 (DE-588)121230538 |4 aut | |
| 245 | 1 | 0 | |a Universal algebra |c P. M. Cohn |
| 250 | |a Rev. ed. | ||
| 264 | 1 | |a Dordrecht |b Reidel |c 1981 | |
| 300 | |a XV, 412 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804119884841353216 |
|---|---|
| adam_text | Contents
Notes to the Reader vi
Preface to the Revised Edition xi
Preface xiii
CHAPTER I: SETS AND MAPPINGS
1. The Axioms of Set Theory I
2. Correspondences 9
3. Mappings and Quotient Sets 12
4. Ordered Sets 18
5. Cardinals and Ordinals 28
6. Categories and Functors 36
CHAPTER II: ALGEBRAIC STRUCTURES
1. Closure Systems 41
2. Q Algebras 47
3. The Isomorphism Theorems 57
4. Lattices 63
5. The Lattice of Subalgebras 79
6. The Lattice of Congruences 86
viii Contents
7. Local and Residual Properties 99
8. The Lattice of Categories of Q Algebras 104
CHAPTER III. FREE ALGEBRAS
1. Universal Functors 108
2. Q Word Algebras 116
3. Clones of Operations 126
4. Representations in Categories of Q Algebras 132
5. Free Algebras in Categories of Q Algebras 137
6. Free and Direct Composition of Q Algebras 142
7. Derived Operators 145
8. Presentations of Q Algebras 150
9. The Word Problem 154
CHAPTER IV. VARIETIES
1. Definition and Basic Properties 161
2. Free Groups and Free Rings 165
3. The Generation of Varieties 169
4. Representations in Varieties of Algebras 180
CHAPTER V. RELATIONAL STRUCTURES AND
MODELS
1. Relational Structures over a Predicate Domain 188
2. Boolean Algebras 191
3. Derived Predicates 200
4. Closed Sentence Classes and Axiomatic Model Classes 205
5. Ultraproducts and the Compactness Theorem 209
6. The Model Space 213
CHAPTER VI. AXIOMATIC MODEL CLASSES
1. Reducts and Enlargements 220
2. The Local Determination of Classes 222
3. Elementary Extensions 228
4. p Closed Classes and Quasivarieties 233
5. Classes Admitting Homomorphic Images 236
6. The Characterization of Axiomatic Model Classes 239
Contents ix
CHAPTER VII. APPLICATIONS
1. The Natural Numbers 247
2. Abstract Dependence Relations 252
3. The Division Problem for Semigroups and Rings 263
4. The Division Problem for Groupoids 279
5. Linear Algebras 283
6. Lie Algebras 289
7. Jordan Algebras 297
Foreword to the Supplements 310
CHAPTER VIII. CATEGORY THEORY AND UNIVERSAL
ALGEBRA
1. The Principle of Duality 311
2. Adjoint Pairs of Functors 312
3. Monads 315
4. Algebraic Theories 318
CHAPTER IX. MODEL THEORY AND UNIVERSAL
ALGEBRA
1. Inductive Theories 321
2. Complete Theories and Model Complete Theories 324
3. Model Completions 326
4. The Forcing Companion 328
5. The Model Companion 331
6. Examples 333
CHAPTER X. MISCELLANEOUS FURTHER RESULTS
1. Subdirect Products and Pullbacks 336
2. The Reduction to Binary Operations 338
3. Invariance of the Rank of Free Algebras 339
4. The Diamond Lemma for Rings 341
5. The Embedding of Rings in Skew Fields 342
CHAPTER XL ALGEBRA AN D LANGUAGE TH EORY
1. Introduction ^
x Contents
2. Grammars 346
3. Machines 355
4. Transductions 364
5. Monoids 365
6. Power Series 371
7. Transformational Grammars 379
Bibliography and Name Index 381
List of Special Symbols 401
Subject Index 404
|
| any_adam_object | 1 |
| author | Cohn, Paul M. 1924-2006 |
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| author_facet | Cohn, Paul M. 1924-2006 |
| author_role | aut |
| author_sort | Cohn, Paul M. 1924-2006 |
| author_variant | p m c pm pmc |
| building | Verbundindex |
| bvnumber | BV005697814 |
| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)251692128 (DE-599)BVBBV005697814 |
| discipline | Mathematik |
| edition | Rev. ed. |
| format | Book |
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| id | DE-604.BV005697814 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:33:17Z |
| institution | BVB |
| isbn | 9027712549 9027712131 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003558898 |
| oclc_num | 251692128 |
| open_access_boolean | |
| owner | DE-703 DE-29T DE-188 |
| owner_facet | DE-703 DE-29T DE-188 |
| physical | XV, 412 S. graph. Darst. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Reidel |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Cohn, Paul M. 1924-2006 Verfasser (DE-588)121230538 aut Universal algebra P. M. Cohn Rev. ed. Dordrecht Reidel 1981 XV, 412 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 6 Algebraische Struktur (DE-588)4001166-5 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Universelle Algebra (DE-588)4061777-4 gnd rswk-swf Algebraische Struktur (DE-588)4001166-5 s Universelle Algebra (DE-588)4061777-4 s 1\p DE-604 Algebra (DE-588)4001156-2 s 2\p DE-604 Mathematics and its applications 6 (DE-604)BV008163334 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003558898&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cohn, Paul M. 1924-2006 Universal algebra Mathematics and its applications Algebraische Struktur (DE-588)4001166-5 gnd Algebra (DE-588)4001156-2 gnd Universelle Algebra (DE-588)4061777-4 gnd |
| subject_GND | (DE-588)4001166-5 (DE-588)4001156-2 (DE-588)4061777-4 |
| title | Universal algebra |
| title_auth | Universal algebra |
| title_exact_search | Universal algebra |
| title_full | Universal algebra P. M. Cohn |
| title_fullStr | Universal algebra P. M. Cohn |
| title_full_unstemmed | Universal algebra P. M. Cohn |
| title_short | Universal algebra |
| title_sort | universal algebra |
| topic | Algebraische Struktur (DE-588)4001166-5 gnd Algebra (DE-588)4001156-2 gnd Universelle Algebra (DE-588)4061777-4 gnd |
| topic_facet | Algebraische Struktur Algebra Universelle Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003558898&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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