Galois Theory (Second Edition)

Cover Page
......Page 1
Contents
......Page 3
B. Vector Spaces
......Page 4
C. Homogeneous Linear Equations
......Page 5
D. Dependence and Independence of Vectors
......Page 7
E. Non-homogeneous Linear Equations
......Page 12
F. Determinants
......Page 14
A. Extension Fields
......Page 24
B. Polynomials
......Page 25
C. Algebraic Elements
......Page 28
D. Splitting Fields
......Page 33
E. Unique Decomposition of Polynomials into Irreducible Factors
......Page 36
F. Group Characters
......Page 37
G. Applications and Examples to Theorem 13
......Page 41
H. Normal Extensions
......Page 44
I. Finite Fields
......Page 52
J. Roots of Unity
......Page 59
K. Noether Equations
......Page 60
L. Kummer's Fields
......Page 62
M. Simple Extensions
......Page 67
N. Existence of a Normal Basis
......Page 69
O. Theorem on Natural Irrationalities
......Page 70
A. Solvable Groups
......Page 72
B. Permutation Groups
......Page 73
C. Solution of Equations by Radicals
......Page 75
D. The General Equation of Degree n......Page 77
E. Solvable Equations of Prime Degree
......Page 79
F. Ruler and Compass Constructions
......Page 83