Author | Cohn, P. M. author |
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Title | Universal Algebra [electronic resource] / by P. M. Cohn |
Imprint | Dordrecht : Springer Netherlands, 1981 |
Connect to | http://dx.doi.org/10.1007/978-94-009-8399-1 |
Descript | XVI, 412 p. online resource |
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