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＜電子ブック＞
Galois Theory / by Steven H. Weintraub
(Universitext. ISSN:21916675)

版	2nd ed. 2009.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	XIV, 212 p : online resource
著者標目	*Weintraub, Steven H author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Algebraic fields LCSH:Polynomials LCSH:Group theory LCSH:Number theory FREE:Algebra FREE:Field Theory and Polynomials FREE:Group Theory and Generalizations FREE:Number Theory
一般注記	to Galois Theory -- Field Theory and Galois Theory -- Development and Applications of Galois Theory -- Extensions of the Field of Rational Numbers -- Further Topics in Field Theory -- Transcendental Extensions The book discusses classical 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 discusses algebraic closure and infinite Galois extensions, and concludes with a new chapter on transcendental extensions. Key topics and features of this second edition: - Approaches Galois theory from the linear algebra point of view, following Artin; - 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. Review from the first edition: "The text offers the standard material of classical field theory and Galois theory, though in a remarkably original, unconventional and comprehensive manner … . the book under review must be seen as a highly welcome and valuable complement to existing textbook literature … . It comes with its own features and advantages … it surely is a perfect introduction to this evergreen subject. The numerous explaining remarks, hints, examples and applications are particularly commendable … just as the outstanding clarity and fullness of the text." (Zentralblatt MATH, Vol. 1089 (15), 2006) Steven H. Weintraub is a Professor of Mathematics at Lehigh University and the author of seven books. This book grew out of a graduate course he taught at Lehigh. He is also the author of Algebra: An Approach via Module Theory (with W. A. Adkins) HTTP:URL=https://doi.org/10.1007/978-0-387-87575-0

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