Book:Emil Artin/Galois Theory/Second Edition With Additions and Revisions

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Emil Artin and Arthur N. Milgram: Galois Theory (2nd Edition)

Published $1944$, Dover Publications

ISBN 0-486-62342-4 (translated by Arthur N. Milgram).

Second edition of 1942: Emil Artin and Arthur N. Milgram: Galois Theory (translated by Arthur N. Milgram)

Subject Matter

Galois Theory


A. Fields
B. Vector Spaces
C. Homogeneous Linear Equations
D. Dependence and Independence of Vectors
E. Non-homogeneous Linear Equations
F. Determinants
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. Applications and Examples to Theorem 13
H. Normal Extensions
I. Finite Fields
J. Roots of Unity
K. Noether's Equations
L. Kummer's Fields
M. Simple Extensions
N. Existence of a Normal Basis
O. 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