Fields and Galois Theory

John M. Howie - Collection Springer Undergraduate Mathematics Series (SUMS)

226 pages, parution le 31/12/2005

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Résumé

The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra.

This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection.

Topics covered include:

rings and fields
integral domains and polynomials
field extensions and splitting fields
applications to geometry
finite fields
the Galois group
equations

Group theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.

L'auteur - John M. Howie

University of St. Andrews, UK

Sommaire

Preface
Contents
Rings and Fields
Integral Domains and Polynomials
Field Extensions
Applications to Geometry
Splitting Fields
Finite Fields
The Galois Group
Equations and Groups
Some Group Theory
Groups and Equations
Regular Polygons
Solutions
Bibliography
List of Symbols
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	John M. Howie
Collection	Springer Undergraduate Mathematics Series (SUMS)
Parution	31/12/2005
Nb. de pages	226
Format	17,5 x 23,5
Couverture	Broché
Poids	395g
Intérieur	Noir et Blanc
EAN13	9781852339869
ISBN13	978-1-85233-986-9