Field Theory / Edition 2

Field Theory / Edition 2

by Steven Roman
     
 

ISBN-10: 0387276777

ISBN-13: 9780387276779

Pub. Date: 11/17/2005

Publisher: Springer New York

Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes

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Overview

Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials the Kummer theory. This new edition has been completely rewritten in order to improve the pedagogy and to make the text more accessible to graduate students. The exercises have also been improved and a new chapter on ordered fields has been included. About the first edition: " ...the author has gotten across many important ideas and results. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study." -J.N. Mordeson, Zentralblatt "The book is written in a clear and explanatory style. It contains over 235 exercises which provide a challenge to the reader. The book is recommended for a graduate course in field theory as well as for independent study."

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Product Details

ISBN-13:
9780387276779
Publisher:
Springer New York
Publication date:
11/17/2005
Series:
Graduate Texts in Mathematics Series, #158
Edition description:
2nd ed. 2006
Pages:
335
Product dimensions:
9.21(w) x 6.14(h) x 0.81(d)

Table of Contents

Pt. IField extensions
1Polynomials23
2Field extensions41
3Embeddings and separability73
4Algebraic independence93
Pt. IIGalois theory
5Galois theory I : an historical perspective113
6Galois theory II : the theory137
7Galois theory III : the Galios group of a polynomial173
8A field extension as a vector space197
9Finite fields I : basic properties211
10Finite fields II : additional properties225
11The roots of unity239
12Cyclic extensions261
13Solvable extensions269
Pt. IIIThe theory of binomials
14Binomials289
15Families of binomials309
AppMobius inversion319

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