ISBN-10:
0387289305
ISBN-13:
9780387289304
Pub. Date:
12/08/2005
Publisher:
Springer New York
Algebra: Volume I: Fields and Galois Theory / Edition 1

Algebra: Volume I: Fields and Galois Theory / Edition 1

by Falko Lorenz, Silvio LevyFalko Lorenz

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Overview

This translation of the 1987 German edition is an introduction into the classical parts of algebra with a focus on fields and Galois theory. It discusses nonstandard topics, such as the transcendence of pi, and new concepts are defined in the framework of the development of carefully selected problems. It includes an appendix with exercises and notes on the previous parts of the book, and brief historical comments are scattered throughout.

Product Details

ISBN-13: 9780387289304
Publisher: Springer New York
Publication date: 12/08/2005
Series: Universitext , #1
Edition description: 2006
Pages: 296
Sales rank: 1,045,783
Product dimensions: 6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Constructibility with Ruler and Compass.- Algebraic Extensions.- Simple Extensions.- Fundamentals of Divisibility.- Prime Factorization in Polynomial Rings. Gauss’s Theorem.- Polynomial Splitting Fields.- Separable Extensions.- Galois Extensions.- Finite Fields, Cyclic Groups and Roots of Unity.- Group Actions.- Applications of Galois Theory to Cyclotomic Fields.- Further Steps into Galois Theory.- Norm and Trace.- Binomial Equations.- Solvability of Equations.- Integral Ring Extensions with Applications to Galois Theory.- The Transcendence of ?.- Fundamentals of Transcendental Field Extensions.- Hilbert’s Nullstellensatz.

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