04581nmm a2200289 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001500139245006100154250001700215260004800232300003200280505061300312505098800925505098501913653001202898041001902910989003802929490003702967028003003004856007203034082000803106520117703114EB000714046EBX0100000000000000056712800000000000000.0cr|||||||||||||||||||||140122 ||| eng a97894009839911 aCohn, P.M.00aUniversal AlgebrahElektronische Ressourcecby P.M. Cohn a1st ed. 1981 aDordrechtbSpringer Netherlandsc1981, 1981 aXVI, 412 pbonline resource0 a2. 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 Symbols0 a1. 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 -- 0 aI: 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 -- aAlgebra07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aMathematics and Its Applications50a10.1007/978-94-009-8399-140uhttps://doi.org/10.1007/978-94-009-8399-1?nosfx=yxVerlag3Volltext0 a512 aThe present book was conceived as an introduction for the user of universal algebra, rather than a handbook for the specialist, but when the first edition appeared in 1965, there were practically no other books entir~ly devoted to the subject, whether introductory or specialized. Today the specialist in the field is well provided for, but there is still a demand for an introduction to the subject to suit the user, and this seemed to justify a reissue of the book. Naturally some changes have had to be made; in particular, I have corrected all errors that have been brought to my notice. Besides errors, some obscurities in the text have been removed and the references brought up to date. I should like to express my thanks to a number of correspondents for their help, in particular C. G. d'Ambly, W. Felscher, P. Goralcik, P. J. Higgins, H.-J. Hoehnke, J. R. Isbell, A. H. Kruse, E. J. Peake, D. Suter, J. S. Wilson. But lowe a special debt to G. M. Bergman, who has provided me with extensivecomments. particularly on Chapter VII and the supplementary chapters. I have also conĀ sulted reviews of the first edition, as well as the Italian and Russian translations