Galois theory 伽罗瓦理论
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内容提要：
In the nineteenth century, French mathematician Evariste Galois developed the Galois theory of groups---one of the most penetrating concepts in mod-ern mathematics. The elements of the theory are clearly presented in this second, revised edition of a volume of lectures delivered by noted mathe-matician 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, veetor spaces,homogeneous linear equations, determinants, and other topics. A second sec-tion considers extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, Noether equa-tions, Jummer's fields, and more. 喜欢读"这本书"的人也喜欢：
目录：
Ⅰ LINEAR ALGEBRA
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 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 |
