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Modern Algebra

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Author(s): Seth Warner
Series: PRENTICE-HALL MATHEMATICS SERIES
Edition: 1
Publisher: Prentice Hall
Year: 1965

Language: English
Commentary: Original Version in 1965
Pages: 348
City: Englewood Cliffs

Chapter VII. THE REAL AND COMPLEX NUMBER FIELDS 459
41. Dedekind and Archimedian Ordered Fields 459
42. The Construction of a Dedekind Ordered Field 469
43. Isomorphisms of Archimedian Ordered Groups 477
44. The Field of Complex Numbers 487
45. The Algebra of Quaternions 503

Chapter VIII. ALGEBRAIC EXTENSIONS OF FIELDS 512
46. Algebraic Extensions 512
47. Constructions by Ruler and Compass 520
48. Galois Theory 527
49. Separable and Normal Extensions 538
50. Roots of Unity 549
51. Solving Quadratics, Cubics, and Quartics 564
52. Permutation Groups 580
53. Solving Polynomials by Radicals 595

Chapter IX. LINEAR OPERATORS 610
54. Diagonalizable Operators 610
55. Primary and Torsion-free Modules 627
56. Finitely Generated Modules 643
57. Decompositions of Linear Operators 659
58. Determinants 679

Chapter X. INNER PRODUCT SPACES 709
59. Inner Products 709
60. Orthonormal Bases 721
61. Adjoints 731
62. The Spectral Theorem 741
63. Linear Operators on Inner Product Spaces 757

Chapter XI. THE AXIOM OF CHOICE
64. The Axiom of Choice 770
65. Zorn’s Lemma 775
66. Algebraic Closures 791
LIST OF SYMBOLS 799
INDEX 801