Galois Theory
Weintraub S.H.
Classical Galois theory is a subject generally acknowledged to be one of the most central and beautiful areas in pure mathematics. This text develops the subject systematically and from the beginning, requiring of the reader only basic facts about polynomials and a good knowledge of linear algebra. Key topics and features of this book:Approaches Galois theory from the linear algebra point of view, following Artin;Develops the basic concepts and theorems of Galois theory, including algebraic, normal, separable, and Galois extensions, and the Fundamental Theorem of Galois Theory;Presents a number of applications of Galois theory, including symmetric functions, finite fields, cyclotomic fields, algebraic number fields, solvability of equations by radicals, and the impossibility of solution of the three geometric problems of Greek antiquity;Provides excellent motivaton and examples throughout.The book discusses Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While most of the book is concerned with finite extensions, it concludes with a discussion of the algebraic closure and of infinite Galois extensions.
Thể loại:
Năm:
2006
Nhà xuát bản:
Springer
Ngôn ngữ:
english
Trang:
194
ISBN 10:
0387289178
ISBN 13:
9780387289175
Loạt:
Universitext
File:
PDF, 8.30 MB
IPFS:
,
english, 2006
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