Algebra / Thomas W. Hungerford.
Series Graduate texts in mathematics ; 73Editor: New York : Springer, 1984, c1974Edición: [Corr.] 3rd printDescripción: xxiii, 502 p. ; 25 cmISBN: 0387905189; 3540905189 (Berlin)Tema(s): AlgebraOtra clasificación: 00A05 (15-01 16-01) Recursos en línea: Google Book SearchPreface ix Acknowledgments xiii Suggestions on the Use of This Book xv Introduction: Prerequisitesand Preliminaries [1] 1. Logic [1] 2. Sets and Classes [1] 3. Functions [3] 4. Relations and Partitions [6] 5. Products [7] 6. The Integers [9] 7. The Axiom of Choice, Order and Zorn’s Lemma [12] 8. Cardinal Numbers [15] Chapter I: Groups [23] 1. Semigroups, Monoids and Groups [24] 2. Homomorphisms and Subgroups [30] 3. Cyclic Groups [35] 4. Cosets and Counting [37] 5. Normality, Quotient Groups, and Homomorphisms [41] 6. Symmetric, Alternating, and Dihedral Groups [46] 7. Categories: Products, Coproducts, and Free Objects [52] 8. Direct Products and Direct Sums [59] 9. Free Groups, Free Products, Generators & Relations [64] Chapter II: The Structure of Groups [70] 1. Free Abelian Groups [70] I 2. Finitely Generated Abelian Groups [76] 3. The Krull-Schmidt Theorem [83] 4. The Action of a Group on a Set [88] 5. The Sylow Theorems [92] 6. Classification of Finite Groups [96] 7. Nilpotent and Solvable Groups [100] 8. Normal and Subnormal Series [107] Chapter III: Rings [114] 1. Rings and Homomorphisms [115] 2. Ideals [122] 3. Factorization in Commutative Rings [135] 4. Rings of Quotients and Localization [142] 5. Rings of Polynomials and Formal Power Series [149] 6. Factorization in Polynomial Rings [157] Chapter IV: Modules [168] 1. Modules, Homomorphisms and Exact Sequences [169] 2. Free Modules and Vector Spaces [180] 3. Projective and Injective Modules [190] 4. Hom and Duality [199] 5. Tensor Products [207] 6. Modules over a Principal Ideal Domain [218] 7. Algebras [226] Chapter V: Fields and Galois Theory [230] 1. Field Extensions [231] Appendix: Ruler and Compass Constructions [238] 2. The Fundamental Theorem [243] Appendix: Symmetric Rational Functions [252] 3. Splitting Fields, Algebraic Closure and Normality [257] Appendix : The Fundamental Theorem of Algebra [265] 4. The Galois Group of a Polynomial [269] 5. Finite Fields [278] 6. Separability [282] 7. Cyclic Extensions [289] 8. Cyclotomic Extensions [297] 9. Radical Extensions [302] Appendix: The General Equation of Degree [307] Chapter VI: The Structure of Fields [311] 1. Transcendence Bases [311] 2. Linear Disjointness and Separability [318] ChapterVII: Linear Algebra [327] 1. Matrices and Maps [328] 2. Rank and Equivalence [335] Appendix: Abelian Groups Defined by Generators and Relations [343] 3. Determinants [348] 4. Decomposition of a Single Linear Transformation and Similarity. [355] 5. The Characteristic Polynomial, Eigenvectors and Eigenvalues [366] Chapter VIII: Commutative Rings and Modules [371] 1. Chain Conditions [372] 2. Prime and Primary Ideals [377] 3. Primary Decomposition [383] 4. Noetherian Rings and Modules [387] 5. Ring Extensions [394] 6. Dedekind Domains [400] 7. The Hilbert Nullstellensatz [409] Chapter IX: The Structure of Rings [414] 1. Simple and Primitive Rings [415] I 2. The Jacobson Radical [424] 3. Semisimple Rings [434] 4. The Prime Radical; Prime and Semiprime Rings [444] 5. Algebras [450] 6. Division Algebras [456] Chapter X: Categories [464] 1. Functors and Natural Transformations [465] 2. Adjoint Functors [476] 3. Morphisms [480] List of Symbols [485] Bibliography [489] Index [493]
Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Libros | Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A05A H936-3 (Browse shelf) | Available | A-5996 |
Browsing Instituto de Matemática, CONICET-UNS shelves, Shelving location: Libros ordenados por tema Close shelf browser
00A05A H572t-2 Topics in algebra / | 00A05A H656 A course in modern algebra / | 00A05A H874 Elements of modern algebra / | 00A05A H936-3 Algebra / | 00A05A H936-8 Algebra / | 00A05A K29 Algebra : | 00A05A K76-3 Einführung in die Algebra. |
Reimpresión de la ed. publicada por Springer en 1980. Originalmente publicado: Holt, Rinehart and Winston, 1974.
Incluye referencias bibliográficas (p. 489-492) e índice.
Preface ix --
Acknowledgments xiii --
Suggestions on the Use of This Book xv --
Introduction: Prerequisitesand Preliminaries [1] --
1. Logic [1] --
2. Sets and Classes [1] --
3. Functions [3] --
4. Relations and Partitions [6] --
5. Products [7] --
6. The Integers [9] --
7. The Axiom of Choice, Order and Zorn’s Lemma [12] --
8. Cardinal Numbers [15] --
Chapter I: Groups [23] --
1. Semigroups, Monoids and Groups [24] --
2. Homomorphisms and Subgroups [30] --
3. Cyclic Groups [35] --
4. Cosets and Counting [37] --
5. Normality, Quotient Groups, and Homomorphisms [41] --
6. Symmetric, Alternating, and Dihedral Groups [46] --
7. Categories: Products, Coproducts, and Free Objects [52] --
8. Direct Products and Direct Sums [59] --
9. Free Groups, Free Products, Generators & Relations [64] --
Chapter II: The Structure of Groups [70] --
1. Free Abelian Groups [70] --
I 2. Finitely Generated Abelian Groups [76] --
3. The Krull-Schmidt Theorem [83] --
4. The Action of a Group on a Set [88] --
5. The Sylow Theorems [92] --
6. Classification of Finite Groups [96] --
7. Nilpotent and Solvable Groups [100] --
8. Normal and Subnormal Series [107] --
Chapter III: Rings [114] --
1. Rings and Homomorphisms [115] --
2. Ideals [122] --
3. Factorization in Commutative Rings [135] --
4. Rings of Quotients and Localization [142] --
5. Rings of Polynomials and Formal Power Series [149] --
6. Factorization in Polynomial Rings [157] --
Chapter IV: Modules [168] --
1. Modules, Homomorphisms and Exact Sequences [169] --
2. Free Modules and Vector Spaces [180] --
3. Projective and Injective Modules [190] --
4. Hom and Duality [199] --
5. Tensor Products [207] --
6. Modules over a Principal Ideal Domain [218] --
7. Algebras [226] --
Chapter V: Fields and Galois Theory [230] --
1. Field Extensions [231] --
Appendix: Ruler and Compass Constructions [238] --
2. The Fundamental Theorem [243] --
Appendix: Symmetric Rational Functions [252] --
3. Splitting Fields, Algebraic Closure and Normality [257] --
Appendix : The Fundamental Theorem of Algebra [265] --
4. The Galois Group of a Polynomial [269] --
5. Finite Fields [278] --
6. Separability [282] --
7. Cyclic Extensions [289] --
8. Cyclotomic Extensions [297] --
9. Radical Extensions [302] --
Appendix: The General Equation of Degree [307] --
Chapter VI: The Structure of Fields [311] --
1. Transcendence Bases [311] --
2. Linear Disjointness and Separability [318] --
ChapterVII: Linear Algebra [327] --
1. Matrices and Maps [328] --
2. Rank and Equivalence [335] --
Appendix: Abelian Groups Defined by --
Generators and Relations [343] --
3. Determinants [348] --
4. Decomposition of a Single Linear Transformation and Similarity. [355] --
5. The Characteristic Polynomial, Eigenvectors and Eigenvalues [366] --
Chapter VIII: Commutative Rings and Modules [371] --
1. Chain Conditions [372] --
2. Prime and Primary Ideals [377] --
3. Primary Decomposition [383] --
4. Noetherian Rings and Modules [387] --
5. Ring Extensions [394] --
6. Dedekind Domains [400] --
7. The Hilbert Nullstellensatz [409] --
Chapter IX: The Structure of Rings [414] --
1. Simple and Primitive Rings [415] --
I 2. The Jacobson Radical [424] --
3. Semisimple Rings [434] --
4. The Prime Radical; Prime and Semiprime Rings [444] --
5. Algebras [450] --
6. Division Algebras [456] --
Chapter X: Categories [464] --
1. Functors and Natural Transformations [465] --
2. Adjoint Functors [476] --
3. Morphisms [480] --
List of Symbols [485] --
Bibliography [489] --
Index [493] --
MR, 82a:00006
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