Universal Algebra
Kluwer Academic Publishers (Verlag)
978-90-277-1254-7 (ISBN)
I: Sets and Mappings.- 1. The Axioms of Set Theory.- 2. Correspondences.- 3. Mappings and Quotient Sets.- 4. Ordered Sets.- 5. Cardinals and Ordinals.- 6. Categories and Functors.- II: Algebraic Structures.- 1. Closure Systems.- 2. ?-Algebras.- 3. The Isomorphism Theorems.- 4. Lattices.- 5. The Lattice of Subalgebras.- 6. The Lattice of Congruences.- 7. Local and Residual Properties.- 8. The Lattice of Categories of ?-Algebras.- III. Free Algebras.- 1. Universal Functors.- 2. ?-Word Algebras.- 3. Clones of Operations.- 4. Representations in Categories of ?-Algebras.- 5. Free Algebras in Categories of ?-Algebras.- 6. Free and Direct Composition of ?-Algebras.- 7. Derived Operators.- 8. Presentations of ?-Algebras.- 9. The Word Problem.- IV. Varieties.- 1. Definition and Basic Properties.- 2. Free Groups and Free Rings.- 3. The Generation of Varieties.- 4. Representations in Varieties of Algebras.- V. Relational Structures and Models.- 1. Relational Structures over a Predicate Domain.- 2. Boolean Algebras.- 3. Derived Predicates.- 4. Closed Sentence Classes and Axiomatic Model Classes.- 5. Ultraproducts and the Compactness Theorem.- 6. The Model Space.- VI. Axiomatic Model Classes.- 1. Reducts and Enlargements.- 2. The Local Determination of Classes.- 3. Elementary Extensions.- 4. p-Closed Classes and Quasivarieties.- 5. Classes Admitting Homomorphic Images.- 6. The Characterization of Axiomatic Model Classes.- VII. Applications.- 1. The Natural Numbers.- 2. Abstract Dependence Relations.- 3. The Division Problem for Semigroups and Rings.- 4. The Division Problem for Groupoids.- 5. Linear Algebras.- 6. Lie Algebras.- 7. Jordan Algebras.- Foreword to the Supplements.- VIII. Category Theory and Universal Algebra.- 1. The Principle of Duality.- 2. Adjoint Pairs of Functors.- 3. Monads.- 4. Algebraic Theories.- IX. Model Theory and Universal Algebra.- 1. Inductive Theories.- 2. Complete Theories and Model Complete Theories.- 3. Model Completions.- 4. The Forcing Companion.- 5. The Model Companion.- 6. Examples.- X. Miscellaneous Further Results.- 1. Subdirect Products and Pullbacks.- 2. The Reduction to Binary Operations.- 3. Invariance of the Rank of Free Algebras.- 4. The Diamond Lemma for Rings.- 5. The Embedding of Rings in Skew Fields.- XI. Algebra and Language Theory.- 1. Introduction.- 2. Grammars.- 3. Machines.- 4. Transductions.- 5. Monoids.- 6. Power Series.- 7. Transformational Grammars.- Bibliography and Name Index.- List of Special Symbols.
Reihe/Serie | Mathematics and Its Applications ; 6 | Mathematics and Its Applications ; 6 |
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Zusatzinfo | XVI, 412 p. |
Verlagsort | Dordrecht |
Sprache | englisch |
Maße | 216 x 279 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
ISBN-10 | 90-277-1254-9 / 9027712549 |
ISBN-13 | 978-90-277-1254-7 / 9789027712547 |
Zustand | Neuware |
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