Classical Galois theory : with examples / Lisl Gaal.

Por: Gaal, Lisl, 1924-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)
Contenidos:
 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]
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Libros Libros Instituto de Matemática, CONICET-UNS
Libros ordenados por tema 12 G111-2 (Browse shelf) Available A-3720

EXTENSIONES ALGEBRAICAS Y TEORÍA DE GALOIS


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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