Modern algebra. Volume I / by B. L. van der Waerden ; in part a development from lectures by E. Artin and E. Noether ; translated from the 2d. rev. German ed. by Fred Blum, with revisions and additions by the author.
Idioma: Inglés Lenguaje original: Alemán Editor: New York : Frederick Ungar, c1953, c1949Descripción: xii, 264 p. ; 24 cm. 25 cmOtra clasificación: 00A05CONTENTS I Introduction xi CHAPTER I NUMBERS AND SETS I 1. Sets [1] I 2. Mappings. Cardinality [2] I 3. The Number Sequence [3] 4. Finite and Countable (Denumerable) Sets [7] I 5. Partitions [9] CHAPTER II GROUPS 6. The Group Concept [11] 7. Subgroups [18] 8. Complexes. Cosets [22] 9. Isomorphisms and Automorphisms [24] 10. Homomorphisms. Normal Divisors. Factor Groups [27] CHAPTER III RINGS AND FIELDS 11. Rings [32] 12. Homomorphism and Isomorphism [38] 13. The Concept of a Field of Quotients [39] 14. Vector Spaces and Hypercomplex Systems [42] 15. Polynomial Rings [45] 16. Ideals. Residue Class Rings [49] 17. Divisibility. Prime Ideals [53] 18. Euclidean Rings and Principal Ideal Rings [55] 19. Factorization [58] CHAPTER IV POLYNOMIALS 20. Differentiation [63] 21. The Zeros of a Polynomial [64] 22. Interpolation Formulae [66] 23. Factorization [70] 24. Irreducibility Criteria [74] 25. Factorization in a Finite Number of Steps [77] 26. Symmetric Functions [78] 27. The Resultant of Two Polynomials [83] 28. The Resultant as a Symmetric Function of the Roots [86] 29. Partial Fraction Decomposition [88] CHAPTER V THEORY OF FIELDS 30. Subfields. Prime Fields [91] 31. Adjunction [93] 32. Simple Field Extensions [94] 33. Linear Dependence over a Skew Field [99] 34. Linear Equations over a Skew Field [104] 35. Algebraic Field Extensions [106] 36. Roots of Unity 1ll 37. Galois Fields (Finite Commutative Fields) [115] 38. Separable and Inseparable Extensions [119] 39. Perfect and Imperfect Fields [124] 40. Simplicity of Algebraic Extensions. Theorem of the Primitive Element [126] 41. Norms and Traces [128] 42. The Field-theoretical Operations in a Finite Number of Steps [134] CHAPTER VI CONTINUATION OF GROUP THEORY 43. Groups with Operators [138] 44. Operator Isomorphism and Operator Homomorphism [140] 45. The Two Laws of Isomorphism [141] 46. Normal Series and Composition Series [142] 47. Direct Products [146] 48. Simplicity of the Alternating Group [149] 49. Transitivity and Primitivity [150] CHAPTER VII THE GALOIS THEORY 50. The Galois Group [153] 51. The Fundamental Theorem of the Calois Theory [156] 52. Conjugate Groups, Conjugate Fields and Elements [159] 53. Cyclotomic Fields [160] 54. The Periods of the Cyclotomic Equation [163] 55 Cyclic Fields and Pure Equations [168] 56. Solution of Equations by Radicals [172] 57. The General Equation of Degree n [175] 58. Equations of the Second, Third, and Fourth Degrees [177] 59. Constructions with Ruler and Compass [183] 60. Metacyclic Equations of Prime Degree [187] 61. Calculation of the Galois Group. Equations with a Symmetric Group [189] CHAPTER VIII INFINITE FIELD EXTENSIONS 62. Algebraically Closed Fields [193] 63. Simple Transcendental Extensions [197] 64. The Degree of Transcendence [200] 65. Differentiation of Algebraic Functions [202] CHAPTER IX REAL FIELDS 66. Ordered Fields [209] 67. Definition of the Real Numbers [211] 68. Zeros of Real Functions [218] 69. The Field of Complex Numbers [222] 70. Algebraic Theory of Real Fields [225] 71. Existence Theorems for Formally-Real Fields [229] 72. Sums of Squares [233] CHAPTER X FIELDS WITH VALUATIONS 73. Valuations [235] 74. Complete Field Extensions [240] 75. Valuations of the Field of Rational Numbers [244] 76. Valuation of Algebraic Extension Fields [248] 77. Valuations of Algebraic Number Fields [255] INDEx [259]
| Item type | Home library | Shelving location | Call number | Materials specified | Copy number | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A05A W127m-2 (Browse shelf) | Vol. I | Available | A-1039 | |||
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Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A05A W127m-2 (Browse shelf) | Vol. I | Ej. 2 | Available | A-2054 |
Traducción de: Moderne Algebra, c1931, 1937, 1940 by Julius Springer, Berlin.
CONTENTS --
I Introduction xi --
CHAPTER I --
NUMBERS AND SETS --
I 1. Sets [1] --
I 2. Mappings. Cardinality [2] --
I 3. The Number Sequence [3] --
4. Finite and Countable (Denumerable) Sets [7] --
I 5. Partitions [9] --
CHAPTER II --
GROUPS --
6. The Group Concept [11] --
7. Subgroups [18] --
8. Complexes. Cosets [22] --
9. Isomorphisms and Automorphisms [24] --
10. Homomorphisms. Normal Divisors. Factor Groups [27] --
CHAPTER III --
RINGS AND FIELDS --
11. Rings [32] --
12. Homomorphism and Isomorphism [38] --
13. The Concept of a Field of Quotients [39] --
14. Vector Spaces and Hypercomplex Systems [42] --
15. Polynomial Rings [45] --
16. Ideals. Residue Class Rings [49] --
17. Divisibility. Prime Ideals [53] --
18. Euclidean Rings and Principal Ideal Rings [55] --
19. Factorization [58] --
CHAPTER IV --
POLYNOMIALS --
20. Differentiation [63] --
21. The Zeros of a Polynomial [64] --
22. Interpolation Formulae [66] --
23. Factorization [70] --
24. Irreducibility Criteria [74] --
25. Factorization in a Finite Number of Steps [77] --
26. Symmetric Functions [78] --
27. The Resultant of Two Polynomials [83] --
28. The Resultant as a Symmetric Function of the Roots [86] --
29. Partial Fraction Decomposition [88] --
CHAPTER V --
THEORY OF FIELDS --
30. Subfields. Prime Fields [91] --
31. Adjunction [93] --
32. Simple Field Extensions [94] --
33. Linear Dependence over a Skew Field [99] --
34. Linear Equations over a Skew Field [104] --
35. Algebraic Field Extensions [106] --
36. Roots of Unity 1ll --
37. Galois Fields (Finite Commutative Fields) [115] --
38. Separable and Inseparable Extensions [119] --
39. Perfect and Imperfect Fields [124] --
40. Simplicity of Algebraic Extensions. Theorem of the Primitive Element [126] --
41. Norms and Traces [128] --
42. The Field-theoretical Operations in a Finite Number of Steps [134] --
CHAPTER VI --
CONTINUATION OF GROUP THEORY --
43. Groups with Operators [138] --
44. Operator Isomorphism and Operator Homomorphism [140] --
45. The Two Laws of Isomorphism [141] --
46. Normal Series and Composition Series [142] --
47. Direct Products [146] --
48. Simplicity of the Alternating Group [149] --
49. Transitivity and Primitivity [150] --
CHAPTER VII --
THE GALOIS THEORY --
50. The Galois Group [153] --
51. The Fundamental Theorem of the Calois Theory [156] --
52. Conjugate Groups, Conjugate Fields and Elements [159] --
53. Cyclotomic Fields [160] --
54. The Periods of the Cyclotomic Equation [163] --
55 Cyclic Fields and Pure Equations [168] --
56. Solution of Equations by Radicals [172] --
57. The General Equation of Degree n [175] --
58. Equations of the Second, Third, and Fourth Degrees [177] --
59. Constructions with Ruler and Compass [183] --
60. Metacyclic Equations of Prime Degree [187] --
61. Calculation of the Galois Group. Equations with a Symmetric Group [189] --
CHAPTER VIII --
INFINITE FIELD EXTENSIONS --
62. Algebraically Closed Fields [193] --
63. Simple Transcendental Extensions [197] --
64. The Degree of Transcendence [200] --
65. Differentiation of Algebraic Functions [202] --
CHAPTER IX --
REAL FIELDS --
66. Ordered Fields [209] --
67. Definition of the Real Numbers [211] --
68. Zeros of Real Functions [218] --
69. The Field of Complex Numbers [222] --
70. Algebraic Theory of Real Fields [225] --
71. Existence Theorems for Formally-Real Fields [229] --
72. Sums of Squares [233] --
CHAPTER X --
FIELDS WITH VALUATIONS --
73. Valuations [235] --
74. Complete Field Extensions [240] --
75. Valuations of the Field of Rational Numbers [244] --
76. Valuation of Algebraic Extension Fields [248] --
77. Valuations of Algebraic Number Fields [255] --
INDEx [259] --
MR, 10,587b
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