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## Topics in algebra / I. N. Herstein.

Editor: New York : Blaisdell, 1964Descripción: viii, 342 p. ; 24 cmOtra clasificación: 00A05
Contenidos:
```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]
6. The Elements of Galois Theory [195]
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]
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
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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