Galois Theory 2nd ed. - E. Artin
TABLE OF CONTENTS
(The sections marked with an asterisk
have been herein added to the content
of the first edition)
Page
1 LINEAR ALGEBRA .................................... 1
A. Fields........................................... 1
B. Vector Spaces .................................... 1
C. Homogeneous Linear Equations ..................... 2
D. Dependence and Independence of Vectors .. , ......... 4
E. Non-homogeneous Linear Equations ................. 9
F.* Determinants ..................................... 11
II FIELD THEORY ............................. <......... 21
A. Extension Fields ................................. 21
B. Polynomials ...................................... 22
C. Algebraic Elements ............................... 25
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
J.
Finite Fields ............................... . .... 49
Roots of Unity ............................. . . .., .. 56
K. Noether Equations ................................ 57
L. Kummer’s Fields ....................... . .......... 59
M. Simple Extensions ................................ 64
N. Existence of a Normal Basis ........... , ........... 66
Q. Theorem on Natural Irrationalities ................... 67
111 APPLICATIONS
By A. N. Milgram., ..................... , ........... 69
A. Solvable Groups .................................. 69
B. Permutation Groups ............................... 70
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 Construction .................... 80
have been herein added to the content
of the first edition)
Page
1 LINEAR ALGEBRA .................................... 1
A. Fields........................................... 1
B. Vector Spaces .................................... 1
C. Homogeneous Linear Equations ..................... 2
D. Dependence and Independence of Vectors .. , ......... 4
E. Non-homogeneous Linear Equations ................. 9
F.* Determinants ..................................... 11
II FIELD THEORY ............................. <......... 21
A. Extension Fields ................................. 21
B. Polynomials ...................................... 22
C. Algebraic Elements ............................... 25
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
J.
Finite Fields ............................... . .... 49
Roots of Unity ............................. . . .., .. 56
K. Noether Equations ................................ 57
L. Kummer’s Fields ....................... . .......... 59
M. Simple Extensions ................................ 64
N. Existence of a Normal Basis ........... , ........... 66
Q. Theorem on Natural Irrationalities ................... 67
111 APPLICATIONS
By A. N. Milgram., ..................... , ........... 69
A. Solvable Groups .................................. 69
B. Permutation Groups ............................... 70
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 Construction .................... 80
