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Introduction to Field Theory - Iain T. Adamson

Introduction to Field Theory

Paperback

Published: 1st November 1982
RRP $56.95
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Field Theory is a fascinating branch of algebra, with many interesting applications, and its central result, the Fundamental Theorem of Galois Theory, is by any standards one of the really important theorems of mathematics. This book brings the reader from the basic definitions to important results and applications, and introduces him to the spirit and some of the techniques of abstract algebra. It is addressed to undergraduates in pure mathematics and presupposes only a little knowledge of elementary group theory. Chapter I develops the elementary properties of rings and fields including the notions of characteristic, prime fields and various types of homomorphisms. In Chapter II extension fields and various ways of classifying them are studies. Chapter III gives an exposition of the Galois Theory, following Artin's approach, and Chapter IV provides a wide variety of applications of the preceding theory. For the second edition Dr Adamson has improved the exposition in places, made corrections and updated the references.

Taken from the hardback review: 'This is an attractive book on field theory and Galois theory...it is very clearly written, with many examples, and the exercises are good...an excellent introduction.' American Mathematical Monthly

Preface
Elementary Definitions
Rings and fields
Elementary properties
Homomorphisms
Vector spaces
Polynomials
Higher polynomial rings trational functions
Extensions of fields
Elementary properties
Simple extensions
Algebraic extensions
Factorisation of polynomials
Splitting fields
Algebraically closed fields
Separable extensions
Galois theory
Automorphisms of fields
Normal extensions
The fundamental theorem of Galois Theory
Norms and traces
The primitive element theorem Lagrange's theorem
Normal bases
Applications
Finite fields
Cyclotomic extensions
Cyclotomic extensions of the rational number field
Cyclic extensions
Wedderburns' theorem
Ruler-an-compasses constructions
Solution by radicals
Generic polynomials
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521286589
ISBN-10: 0521286581
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 192
Published: 1st November 1982
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 20.32 x 12.7  x 1.12
Weight (kg): 0.21
Edition Number: 2
Edition Type: Revised