دانلود کتاب Universal Algebra: Fundamentals and Selected Topics

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Front Cover
Half-Title
Title
Copyright
Author’s Dedication
Contents
Preface
Part I: Fundamentals of Universal Algebra
Chapter 1: Algebras
1.1 Operations
1.2 Examples
1.3 More about subalgebras, homomorphisms and direct products
Exercise Set
1.4 Generating subalgebras
Exercise Set
1.5 Congruences and quotient algebras
Exercise Set
Chapter 2: Lattices
2.1 Ordered sets
Exercise Set
2.2 Distributive and modular lattices
Exercise Set
2.3 Complete lattices
Exercise Set
2.4 Closure operators and algebraic lattices
Exercise Set
2.5 Galois connections
2.6 Ideals in lattices
Exercise Set
Chapter 3: The Nuts and Bolts of Universal Algebra
3.1 The isomorphism theorems
Exercise Set
3.2 Direct products
Exercise Set
3.3 Subdirect products
Exercise Set
3.4 Case studies
Exercise Set
3.5 Varieties and other classes of algebras
Exercise Set
Chapter 4: Clones, Terms, and Equational Classes
4.1 Clones
Exercise Set
4.2 Invariant relations
Exercise Set
4.3 Terms and free algebras
Exercise Set
4.4 Identities and Birkhoff’s theorem
Exercise Set
4.5 The lattice of subvarieties
Exercise Set
4.6 Equational theories and fully invariant congruences
Exercise Set
4.7 Maltsev conditions
Exercise Set
4.8 Interpretations
Exercise Set
Part II: Selected Topics
Introduction to Part II
Chapter 5: Congruence Distributive Varieties
5.1 Ultrafilters and ultraproducts
Exercise Set
5.2 Jónsson’s lemma
Exercise Set
5.3 Model theory
Exercise Set
5.4 Finitely based and nonfinitely based algebras
5.5 Definable principal (sub)congruences
Exercise Set
Chapter 6: Arithmetical Varieties
6.1 Large clones
Exercise Set
6.2 How rare are primal algebras?
Chapter 7: Maltsev Varieties
7.1 Directly representable varieties
Exercise Set
7.2 The centralizer congruence
Exercise Set
7.3 Abelian varieties
Exercise Set
7.4 Commutators
Exercise Set
7.5 Directly representable varieties revisited
Exercise Set
7.6 Minimal varieties
Exercise Set
7.7 Functionally complete algebras
Exercise Set
Chapter 8: Finite Algebras and Locally Finite Varieties
8.1 Minimal algebras
8.2 Localization and induced algebras
Exercise Set
8.3 Centralizers again!
Exercise Set
8.4 Applications
Bibliography