Topics in algebra / I. N. Herstein.
Editor: New York : Blaisdell, 1964Descripción: viii, 342 p. ; 24 cmOtra clasificación: 00A051. Preliminary Notions 1. Set Theory [2] 2. Mappings [9] 3. The Integers [17] 2. Group Theory 1. Definition of a Group [26] 2. Some Examples of Groups [27] 3. Some Preliminary Lemmas [29] 4. Subgroups [32] 5. A Counting Principle [38] 6. Normal Subgroups and Quotient Groups [41] 7. Homomorphisms [46] 8. Automorphisms [56] 9. Cayley’s Theorem [60] 10. Permutation Groups [64] 11. Another Counting Principle [69] 12. Sylow’s Theorem [78] 3. Ring Theory 1. Definition and Examples of Rings [83] 2. Some Special Classes of Rings [88] 3. Homomorphisms [92] 4. Ideals and Quotient Rings [94] 5. More Ideals and Quotient Rings [98] 6. The Field of Quotients of an Integral Domain [101] 7. Euclidean Rings [104] 8. A Particular Euclidean Ring [110] 9. Polynomial Rings [113] 10, Polynomials Over the Rational Field [120] 11. Polynomial Rings Over Commutative Rings [122] 4. Vector Spaces and Modules 1. Elementary Basic Concepts [130] 2. Linear Independence and Bases [136] 3. Dual Spaces [144] 4. Inner Product Space [150] 5. Modules [160] 5. Fields 1. Extension Fields [167] 2. The Transcendence of e [175] 3. Roots of Polynomials [179] 4. Construction with Straight-Edge and Compass [187] 5. More About Roots [191] 6. The Elements of Galois Theory [195] 7. Solvability by Radicals [208] 6. Linear Transformations 1. The Algebra of Linear Transformations [217] 2. Characteristic Roots [225] 3. Matrices [228] 4. Canonical Forms: Triangular Form [241] 5. Canonical Forms: Nilpotent Transformations [248] 6. Canonical Forms: A Decomposition of V: Jordan Form [255] 7. Canonical Forms: Rational Canonical Form [262] 8. Trace and Transpose [271] 9. Determinants [279] 10. Hermitian, Unitary, and Normal Transformations [294] 11. Real Quadratic Forms [308] 7. Selected Topics 1. Finite Fields [314] 2. Wedderbun’s Theorem on Finite Division Rings [318] 3. A Theorem of Frobenius [326] 4. Integral Quaternions and the Four-Square Theorem [329]
Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
---|---|---|---|---|---|---|---|---|
Libros | Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A05A H572t (Browse shelf) | Available | A-1420 |
1. Preliminary Notions --
1. Set Theory [2] --
2. Mappings [9] --
3. The Integers [17] --
2. Group Theory --
1. Definition of a Group [26] --
2. Some Examples of Groups [27] --
3. Some Preliminary Lemmas [29] --
4. Subgroups [32] --
5. A Counting Principle [38] --
6. Normal Subgroups and Quotient Groups [41] --
7. Homomorphisms [46] --
8. Automorphisms [56] --
9. Cayley’s Theorem [60] --
10. Permutation Groups [64] --
11. Another Counting Principle [69] --
12. Sylow’s Theorem [78] --
3. Ring Theory --
1. Definition and Examples of Rings [83] --
2. Some Special Classes of Rings [88] --
3. Homomorphisms [92] --
4. Ideals and Quotient Rings [94] --
5. More Ideals and Quotient Rings [98] --
6. The Field of Quotients of an Integral Domain [101] --
7. Euclidean Rings [104] --
8. A Particular Euclidean Ring [110] --
9. Polynomial Rings [113] --
10, Polynomials Over the Rational Field [120] --
11. Polynomial Rings Over Commutative Rings [122] --
4. Vector Spaces and Modules --
1. Elementary Basic Concepts [130] --
2. Linear Independence and Bases [136] --
3. Dual Spaces [144] --
4. Inner Product Space [150] --
5. Modules [160] --
5. Fields --
1. Extension Fields [167] --
2. The Transcendence of e [175] --
3. Roots of Polynomials [179] --
4. Construction with Straight-Edge and Compass [187] --
5. More About Roots [191] --
6. The Elements of Galois Theory [195] --
7. Solvability by Radicals [208] --
6. Linear Transformations --
1. The Algebra of Linear Transformations [217] --
2. Characteristic Roots [225] --
3. Matrices [228] --
4. Canonical Forms: Triangular Form [241] --
5. Canonical Forms: Nilpotent Transformations [248] --
6. Canonical Forms: A Decomposition of V: Jordan Form [255] --
7. Canonical Forms: Rational Canonical Form [262] --
8. Trace and Transpose [271] --
9. Determinants [279] --
10. Hermitian, Unitary, and Normal Transformations [294] --
11. Real Quadratic Forms [308] --
7. Selected Topics --
1. Finite Fields [314] --
2. Wedderbun’s Theorem on Finite Division Rings [318] --
3. A Theorem of Frobenius [326] --
4. Integral Quaternions and the Four-Square Theorem [329] --
MR, 30 #2028
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