Classical Galois theory : with examples / Lisl Gaal.
Editor: New York, N.Y. : Chelsea, 1973Edición: 2nd edDescripción: viii, 248 p. ; 26 cmISBN: 082840268XOtra clasificación: 12.40 | 12-01 (10Bxx) | 12-01 (11R32 12F10)CONTENTS Preface V CHAPTER I PREREQUISITES [1] 1.1 Group Theory [1] 1.2 Permutations and Permutation Groups [7] 1.3 Fields [12] 1.4 Rings and Polynomials [14] 1.5 Some Elementary Theory of Equations [22] 1.6 Vector Spaces [29] CHAPTER II FIELDS [33] 2.1 Degree of an Algebraic Extension [33] 2.2 Isomorphisms of Fields [39] 2.3 Automorphisms of Fields [50] 2.4 Fixed Fields [57] CHAPTER III FUNDAMENTAL THEOREM [69] 3.1 Splitting Fields [69] 3.2 Normal Extensions and Groups of Automorphisms [76] 3.3 Conjugate Fields and Elements [88] 3.4 Fundamental Theorem [93] CHAPTER IV APPLICATIONS [121] 4.1 Solvability of Equations [121] 4.2 Solvable Equations Have Solvable Groups [125] 4.3 General Equation of Degree n [136] 4.4 Roots of Unity and Cyclic Equations [139] 4.5 How to Solve a Solvable Equation [157] 4.6 Ruler-and-Compass Constructions [180] 4.7 Lagrange’s Theorem [196] 4.8 Resolvent of a Polynomial [202] 4.9 Calculation of the Galois Group [212] 4.10 Matrix Solutions of Equations [219] 4.11 Finite Fields [222] 4.12 More Applications [233] Bibliography [245] Index [247]
Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Libros | Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 12 G111-2 (Browse shelf) | Available | A-3720 |
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12 En56 A resolução de equações algébricas e o problema inverso da teoria de Galois / | 12 En56t Teoria de Galois infinita / | 12 En56t Teoria de Galois infinita / | 12 G111-2 Classical Galois theory : | 12 G338 7 prácticas de álgebra / | 12 H131 Field theory and its classical problems / | 12 Iw96 Lectures on p-adic L-functions / |
Bibliografía: p. 245.
CONTENTS --
Preface V --
CHAPTER I PREREQUISITES [1] --
1.1 Group Theory [1] --
1.2 Permutations and Permutation Groups [7] --
1.3 Fields [12] --
1.4 Rings and Polynomials [14] --
1.5 Some Elementary Theory of Equations [22] --
1.6 Vector Spaces [29] --
CHAPTER II FIELDS [33] --
2.1 Degree of an Algebraic Extension [33] --
2.2 Isomorphisms of Fields [39] --
2.3 Automorphisms of Fields [50] --
2.4 Fixed Fields [57] --
CHAPTER III FUNDAMENTAL THEOREM [69] --
3.1 Splitting Fields [69] --
3.2 Normal Extensions and Groups of Automorphisms [76] --
3.3 Conjugate Fields and Elements [88] --
3.4 Fundamental Theorem [93] --
CHAPTER IV APPLICATIONS [121] --
4.1 Solvability of Equations [121] --
4.2 Solvable Equations Have Solvable Groups [125] --
4.3 General Equation of Degree n [136] --
4.4 Roots of Unity and Cyclic Equations [139] --
4.5 How to Solve a Solvable Equation [157] --
4.6 Ruler-and-Compass Constructions [180] --
4.7 Lagrange’s Theorem [196] --
4.8 Resolvent of a Polynomial [202] --
4.9 Calculation of the Galois Group [212] --
4.10 Matrix Solutions of Equations [219] --
4.11 Finite Fields [222] --
4.12 More Applications [233] --
Bibliography [245] --
Index [247] --
MR, 43 #6185 (de la 1ª ed.)
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