Galois TheoryCourier Corporation, 1 janv. 1998 - 82 pages 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. |
Table des matières
LINEAR ALGEBRA | 11 |
C Homogeneous Linear Equations | 2 |
D Dependence and Independence of Vectors | 4 |
E Nonhomogeneous Linear Equations | 9 |
F Determinants | 10 |
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 |