Topics in algebra / I. N. Herstein.
Editor: New York : John Wiley, c1975Edición: 2nd edDescripción: xi, 388 p. ; 24 cmISBN: 0471010901Tema(s): AlgebraOtra clasificación: 00A051 Preliminary Notions [1] 1.1 Set Theory [2] 1.2 Mappings [10] 1.3 The Integers [18] Group Theory [26] 2.1 Definition of a Group [27] 2.2 Some Examples of Groups [29] 2.3 Some Preliminary Lemmas [33] 2.4 Subgroups [37] 2.5 A Counting Principle [44] 2.6 Normal Subgroups and Quotient Groups [49] 2.7 Homomorphisms [54] 2.8 Automorphisms [66] 2.9 Cayley’s Theorem [71] 2.10 Permutation Groups [75] 2.11 Another Counting Principle [82] 2.12 Sylow’s Theorem [91] 2.13 Direct Products [103] 2.14 Finite Abelian Groups [109] 3 Ring- Theory [120] 3.1 Definition and Examples of Rings [120] 3.2 Some Special Classes of Rings [125] 3.3 Homomorphisms [131] 3.4 Ideals and Quotient Rings [133] 3.5 More Ideals and Quotient Rings [137] 3.6 The Field of Quotients of an Integral Domain [140] 3.7 Euclidean Rings [143] 3.8 A Particular Euclidean Ring [149] 3.9 Polynomial Rings [153] 3.10 Polynomials over the Rational Field [159] 3.11 Polynomial Rings over Commutative Rings [161] Vector Spaces and Modules [170] 4.1 Elementary Basic Concepts [171] 4.2 Linear Independence and Bases [177] 4.3 Dual Spaces [184] 4.4 Inner Product Spaces [191] 4.5 Modules [201] 5 Fields [207] 5.1 Extension Fields [207] 5.2 The Transcendence of e [216] 5.3 Roots of Polynomials [219] 5.4 Construction with Straightedge and Compass [228] 5.5 More About Roots [232] 5.6 The Elements of Galois Theory [237] 5.7 Solvability by Radicals [250] 5.8 Galois Groups over the Rationals [256] 6 Linear Transformations [260] 6.1 The Algebra of Linear Transformations [261] 6.2 Characteristic Roots [270] 6.3 Matrices [273] 6.4 Canonical Forms: Triangular Form [285] 6.5 Canonical Forms: Nilpotent Transformations [292] 6.6 Canonical Forms: A Decomposition of V: Jordan Form [298] 6.7 Canonical Forms: Rational Canonical Form [305] 6.8 Trace and Transpose [313] 6.9 Determinants [322] 6.10 Hermitian, Unitary, and Normal Transformations [336] 6.11 Real Quadratic Forms. [350] 7 Selected Topics [355] 7.1 Finite Fields [356] 7.2 Wedderburn’s Theorem on Finite Division Rings [360] 7.3 A Theorem of Frobenius [368] 7.4 Integral Quaternions and the Four-Square Theorem [371]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A05A H572t-2 (Browse shelf) | Available | A-8476 |
Incluye bibliografía e índice.
1 Preliminary Notions [1] --
1.1 Set Theory [2] --
1.2 Mappings [10] --
1.3 The Integers [18] --
Group Theory [26] --
2.1 Definition of a Group [27] --
2.2 Some Examples of Groups [29] --
2.3 Some Preliminary Lemmas [33] --
2.4 Subgroups [37] --
2.5 A Counting Principle [44] --
2.6 Normal Subgroups and Quotient Groups [49] --
2.7 Homomorphisms [54] --
2.8 Automorphisms [66] --
2.9 Cayley’s Theorem [71] --
2.10 Permutation Groups [75] --
2.11 Another Counting Principle [82] --
2.12 Sylow’s Theorem [91] --
2.13 Direct Products [103] --
2.14 Finite Abelian Groups [109] --
3 Ring- Theory [120] --
3.1 Definition and Examples of Rings [120] --
3.2 Some Special Classes of Rings [125] --
3.3 Homomorphisms [131] --
3.4 Ideals and Quotient Rings [133] --
3.5 More Ideals and Quotient Rings [137] --
3.6 The Field of Quotients of an Integral Domain [140] --
3.7 Euclidean Rings [143] --
3.8 A Particular Euclidean Ring [149] --
3.9 Polynomial Rings [153] --
3.10 Polynomials over the Rational Field [159] --
3.11 Polynomial Rings over Commutative Rings [161] --
Vector Spaces and Modules [170] --
4.1 Elementary Basic Concepts [171] --
4.2 Linear Independence and Bases [177] --
4.3 Dual Spaces [184] --
4.4 Inner Product Spaces [191] --
4.5 Modules [201] --
5 Fields [207] --
5.1 Extension Fields [207] --
5.2 The Transcendence of e [216] --
5.3 Roots of Polynomials [219] --
5.4 Construction with Straightedge and Compass [228] --
5.5 More About Roots [232] --
5.6 The Elements of Galois Theory [237] --
5.7 Solvability by Radicals [250] --
5.8 Galois Groups over the Rationals [256] --
6 Linear Transformations [260] --
6.1 The Algebra of Linear Transformations [261] --
6.2 Characteristic Roots [270] --
6.3 Matrices [273] --
6.4 Canonical Forms: Triangular Form [285] --
6.5 Canonical Forms: Nilpotent Transformations [292] --
6.6 Canonical Forms: A Decomposition of V: Jordan Form [298] --
6.7 Canonical Forms: Rational Canonical Form [305] --
6.8 Trace and Transpose [313] --
6.9 Determinants [322] --
6.10 Hermitian, Unitary, and Normal Transformations [336] --
6.11 Real Quadratic Forms. [350] --
7 Selected Topics [355] --
7.1 Finite Fields [356] --
7.2 Wedderburn’s Theorem on Finite Division Rings [360] --
7.3 A Theorem of Frobenius [368] --
7.4 Integral Quaternions and the Four-Square Theorem [371] --
MR, 50 #9456
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