Book:Emil Artin/Galois Theory

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Emil Artin and Arthur N. Milgram: Galois Theory

Published $1942$ (translated by Arthur N. Milgram).


Subject Matter

Galois Theory


Contents

I. LINEAR ALGEBRA
A. Fields
B. Vector Spaces
C. Homogeneous Linear Equations
D. Dependence and Independence of Vectors
E. Non-homogeneous Linear Equations
II. Field Theory
A. Extension Fields
B. Polynomials
C. Algebraic Elements
D. Splitting Fields
E. Unique Decomposition of Polynomials into Irreducible Factors
F. Group Characters
G. Normal Extensions
H. Finite Fields
I. Roots of Unity
J. Noether's Equations
K. Kummer's Fields
L. Simple Extensions
M. Existence of a Normal Basis
N. Theorem on Natural Irrationalities
III. Applications (by A.N. Milgram)
A. Solvable Groups
B. Permutation Groups
C. Solution of Equations by Radicals
D. The General Equation of Degree $n$
E. Solvable Equations of Prime Degree
F. Ruler and Compass Construction
Bibliography
Index


Further Editions