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Universal algebra:

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Bibliographic Details
Main Author:	Cohn, Paul M. 1924-2006 (Author)
Format:	Book
Language:	English
Published:	Dordrecht Reidel 1981
Edition:	Rev. ed.
Series:	Mathematics and its applications 6
Subjects:	Algebraische Struktur Algebra Universelle Algebra
Online Access:	Inhaltsverzeichnis
Physical Description:	XV, 412 S. graph. Darst.
ISBN:	9027712549 9027712131

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MARC


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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
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isbn	9027712549 9027712131
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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
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work_keys_str_mv	AT cohnpaulm universalalgebra

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