Galois Theory

Paperback | November 21, 2008

bySteven H. Weintraub

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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).

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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 f...

From the Jacket

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 f...

Steven H. Weintraub is a Professor of Mathematics at Lehigh University and 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).

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Format:PaperbackDimensions:226 pages, 9.25 × 6.1 × 0.39 inPublished:November 21, 2008Publisher:SpringerLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387875743

ISBN - 13:9780387875743

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Table of Contents

Introduction 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.- A. Some Results from Group Theory.- B. A Lemma on Constructing Fields.- C. A Lemma from Elementary Number Theory.- References.- Index.

Editorial Reviews

From the reviews:"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." (Werner Kleinert, Zentralblatt MATH, Vol. 1089 (15), 2006)From the reviews of the second edition:"The book is a valuable reference, covering many more topics than most of the standard books on the subject." (Mowaffaq Hajja, Zentralblatt MATH, Vol. 1195, 2010)