Galois Theory

Steven H. Weintraub - Collection Universitext

200 pages, parution le 17/02/2006

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Résumé

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.

Written for: Undergraduate mathematics students, graduate mathematics students

L'auteur - Steven H. Weintraub

Steven H. Weintraub is Professor and Chair of the Department of Mathematics at Lehigh University. This book, his fifth, grew out of a graduate course he taught at Lehigh. His other books include Algebra: An Approach via Module Theory (with W. A. Adkins).

Sommaire

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
A. Some Results from Group Theory
B. A Lemma on Constructing Fields
C. A Lemma from Elementary Number Theory

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Steven H. Weintraub
Collection	Universitext
Parution	17/02/2006
Nb. de pages	200
Format	15,5 x 23,5
Couverture	Broché
Poids	355g
Intérieur	Noir et Blanc
EAN13	9780387287256
ISBN13	978-0-387-28725-6