Galois Theory

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Courier Corporation, 1944 - Mathematics - 82 pages
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In the nineteenth century, French mathematician Evariste Galois developed the Galois theory of groups-one of the most penetrating concepts in modem mathematics. The elements of the theory are clearly presented in this second, revised edition of a volume of lectures delivered by noted mathematician Emil Artin. The book has been edited by Dr. Arthur N. Milgram, who has also supplemented the work with a Section on Applications.
The first section deals with linear algebra, including fields, vector spaces, homogeneous linear equations, determinants, and other topics. A second section considers extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, Noether equations, Jummer's fields, and more.
Dr. Milgram's section on applications discusses solvable groups, permutation groups, solution of equations by radicals, and other concepts.

  

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Contents

LINEAR ALGEBRA
1
C Homogeneous Linear Equations
2
D Dependence and Independence of Vectors
4
E Nonhomogeneous Linear Equations
9
F Determinants
11
FIELD THEORY
21
B Polynomials
22
C Algebraic Elements
25
J Roots of Unity
56
K Noether Equations
57
L Kummers Fields
59
M Simple Extensions
64
N Existence of a Normal Basis
66
O Theorem on Natural Irrationalities
67
APPLICATIONS
69
B Permutation Groups
70

D Splitting Fields
30
E Unique Decomposition of Polynomials into Irreducible Factors
33
F Group Characters
34
G Applications and Examples to Theorem 13
38
H Normal Extensions
41
I Finite Fields
49
C Solution of Equations by Radicals
72
D The General Equation of Degree n
74
E Solvable Equations of Prime Degree
76
F Ruler and Compass Constructions
80
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