A course in universal algebra / Stanley Burris, H. P. Sankappanavar.
Series Graduate texts in mathematics ; 78Editor: New York : Springer-Verlag, c1981Descripción: xvi, 276 p. : il. ; 25 cmISBN: 0387905782Tema(s): Algebra, UniversalOtra clasificación: 08-01Special Notation xv Preliminaries [1] Chapter I Lattices Definitions of Lattices [3] Isomorphic Lattices, and Sublattices [8] Distributive and Modular Lattices [10] Complete Lattices, Equivalence Relations, and Algebraic Lattices [14] Closure Operators [18] Chapter II The Elements of Universal Algebra Definition and Examples of Algebras [22] Isomorphic Algebras, and Subalgebras [28] Algebraic Lattices and Subuniverses [30] The Irredundant Basis Theorem [32] Congruences and Quotient Algebras [35] Homomorphisms and the Homomorphism and Isomorphism Theorems [42] Direct Products, Factor Congruences, and Directly Indecomposable Algebras [51] Subdirect Products, Subdirectly Irreducible Algebras, and Simple Algebras [56] Class Operators and Varieties [60] Terms, Term Algebras, and Free Algebras [62] Identities, Free Algebras, and Birkhoff’s Theorem [71] Mal’cev Conditions [77] The Center of an Algebra [82] Equational Logic and Fully Invariant Congruences [89] Chapter III Selected Topics Steiner Triple Systems, Squags, and Sloops [99] Quasigroups, Loops, and Latin Squares [102] Orthogonal Latin Squares [103] Finite State Acceptors [107] Chapter IV Starting from Boolean Algebras Boolean Algebras H6 Boolean Rings [122] Filters and Ideals [127] Stone Duality [135] Boolean Powers [141] Ultraproducts and Congruence-distributive Varieties [145] Primal Algebras [150] Boolean Products [154] Discriminator Varieties [164] Quasiprimal Algebras [169] Functionally Complete Algebras and Skew-free Algebras [176] Semisimple Varieties [183] Directly Representable Varieties [187] Chapter V Connections with Model Theory First-order Languages, First-order Structures, and Satisfaction [191] Reduced Products and Ultraproducts [205] Principal Congruence Formulas [221] Three Finite Basis Theorems [227] Semantic Embeddings and Undecidability [237] Recent Developments and Open Problems [249] Bibliography [257] Author Index [267] Subject Index [269]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 08 B971 (Browse shelf) | Available | A-6124 |
Incluye referencias bibliográficas (p. 257-265) e índices.
Special Notation xv --
Preliminaries [1] --
Chapter I --
Lattices --
Definitions of Lattices [3] --
Isomorphic Lattices, and Sublattices [8] --
Distributive and Modular Lattices [10] --
Complete Lattices, Equivalence Relations, and --
Algebraic Lattices [14] --
Closure Operators [18] --
Chapter II --
The Elements of Universal Algebra --
Definition and Examples of Algebras [22] --
Isomorphic Algebras, and Subalgebras [28] --
Algebraic Lattices and Subuniverses [30] --
The Irredundant Basis Theorem [32] --
Congruences and Quotient Algebras [35] --
Homomorphisms and the Homomorphism and --
Isomorphism Theorems [42] --
Direct Products, Factor Congruences, and Directly --
Indecomposable Algebras [51] --
Subdirect Products, Subdirectly Irreducible Algebras, and --
Simple Algebras [56] --
Class Operators and Varieties [60] --
Terms, Term Algebras, and Free Algebras [62] --
Identities, Free Algebras, and Birkhoff’s Theorem [71] --
Mal’cev Conditions [77] --
The Center of an Algebra [82] --
Equational Logic and Fully Invariant Congruences [89] --
Chapter III --
Selected Topics --
Steiner Triple Systems, Squags, and Sloops [99] --
Quasigroups, Loops, and Latin Squares [102] --
Orthogonal Latin Squares [103] --
Finite State Acceptors [107] --
Chapter IV --
Starting from Boolean Algebras --
Boolean Algebras H6 --
Boolean Rings [122] --
Filters and Ideals [127] --
Stone Duality [135] --
Boolean Powers [141] --
Ultraproducts and Congruence-distributive Varieties [145] --
Primal Algebras [150] --
Boolean Products [154] --
Discriminator Varieties [164] --
Quasiprimal Algebras [169] --
Functionally Complete Algebras and Skew-free Algebras [176] --
Semisimple Varieties [183] --
Directly Representable Varieties [187] --
Chapter V --
Connections with Model Theory --
First-order Languages, First-order Structures, and Satisfaction [191] --
Reduced Products and Ultraproducts [205] --
Principal Congruence Formulas [221] --
Three Finite Basis Theorems [227] --
Semantic Embeddings and Undecidability [237] --
Recent Developments and Open Problems [249] --
Bibliography [257] --
Author Index [267] --
Subject Index [269] --
MR, 83k:08001
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