Book:Emil Artin/Galois Theory

Emil Artin and Arthur N. Milgram: Galois Theory

Published $\text {1942}$ (translated by Arthur N. Milgram)

Subject Matter

Galois Theory

Contents

$\text {I}$. LINEAR ALGEBRA

A. Fields

B. Vector Spaces

C. Homogeneous Linear Equations

D. Dependence and Independence of Vectors

E. Non-homogeneous Linear Equations

$\text {II}$. 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

$\text {III}$. 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

• 1944: Emil Artin and Arthur N. Milgram: Galois Theory (2nd ed.)