Univerzitní knihovna OU - Úplné zobrazení záznamu

Preface ix // I Fundamentals of Universal Algebra 1 // 1 Algebras 3 // 1.1 Operations 3 // 1.2 Examples 4 // 1.3 More about subs, homs and prods 7 // 1.4 Generating subalgebras 10 // 1.5 Congruences and quotient algebras 13 // 2 Lattices 21 // 2.1 Ordered sets 21 // 2.2 Distributive and modular lattices 24 // 2.3 Complete lattices 30 // 2.4 Closure operators and algebraic lattices 34 // 2.5 Galois connections 38 // 2.6 Ideals in lattices 40 // 3 The Nuts and Bolts of Universal Algebra 47 // 3.1 The isomorphism theorems 47 // 3.2 Direct products 52 // 3.3 Subdirect products 55 // 3.4 Case studies 60 // 3.5 Varieties and other classes of algebras 71 // 4 Clones, Terms, and Equational Classes 79 // 4.1 Clones 79 // 4.2 Invariant relations 88 // 4.3 Terms and free algebras 94 // 4.4 Identities and Birkhoff’s theorem 104 // 4.5 The lattice of subvarieties Ill // 4.6 Equational theories and fully invariant congruences 117 // 4.7 Maltsev conditions 121 // 4.8 Interpretations 130 // viii // II Selected Topics 135 // 5 Congruence Distributive Varieties 139 // 5.1 Ultrafilters and ultraproducts 139 // 5.2 Jónsson’s lemma 145 // 5.3 Model theory 149 // 5.4 Finitely based and nonfinitely based algebras 156 // 5.5 Definable principal (sub)congruences 160 // 6 Arithmetical Varieties 169 // 6.1 Large clones 169 // 6.2 How rare are primal algebras? 178 // 7 Maltsev Varieties 189 // 7.1 Directly representable varieties 189 // 7.2 The centralizer congruence 197 // 7.3 Abelian varieties 205 // 7.4 Commutators 216 // 7.5 Directly representable varieties revisited 224 // 7.6 Minimal varieties 233 // 7.7 Functionally complete algebras 239 // 8 Finite Algebras and Locally Finite Varieties 245 // 8.1 Minimal algebras 245 // 8.2 Localization and induced algebras 252 // 8.3 Centralizers again! 263 // 8.4 Applications 274 // Bibliography 291 // Index of Notation 299 // Index 303

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