J.-P. Escofier
Galois Theory
"Escofier’s treatment, at a level suitable for advanced, senior undergraduates or first-year graduate students, centers on finite extensions of number fields, incorporating numerous examples and leaving aside finite fields and the entire concept of separability for the final chapters . . . copious, well-chosen exercises . . . are presented with their solutions . . . The prose is . . . spare and enthusiastic, and the proofs are both instructive and efficient . . . Escofier has written an excellent text, offering a relatively elementary introduction to a beautiful subject in a book sufficiently broad to present a contemporary viewpoint and intuition but sufficiently restrained so as not to overwhelm the reader."—AMERICAN MATHEMATICAL SOCIETY
Author(s): Jean-Pierre Escofier (auth.)
Series: Graduate Texts in Mathematics 204
Edition: 1
Publisher: Springer-Verlag New York
Year: 2001
Language: English
Pages: 283
Tags: Algebra; Number Theory
Front Matter....Pages i-xiv
Historical Aspects of the Resolution of Algebraic Equations....Pages 1-7
History of the Resolution of Quadratic, Cubic, and Quartic Equations Before 1640....Pages 9-24
Symmetric Polynomials....Pages 25-50
Field Extensions....Pages 51-77
Constructions with Straightedge and Compass....Pages 79-91
K -Homomorphisms....Pages 93-105
Normal Extensions....Pages 107-117
Galois Groups....Pages 119-148
Roots of Unity....Pages 149-177
Cyclic Extensions....Pages 179-193
Solvable Groups....Pages 195-206
Solvability of Equations by Radicals....Pages 207-217
The Life of Évariste Galois....Pages 219-225
Finite Fields....Pages 227-255
Separable Extensions....Pages 257-260
Recent Developments....Pages 261-269
Back Matter....Pages 271-283
