Fields and Galois Theory - Howie, John M.

Fields and Galois Theory

John M. Howie

Yayınevi: Springer

Yayın tarihi: 10/2007

ISBN: 9781852339869

İngilizce | 225 Sayfa | 17,27 x 23,11 cm

Tür: Matematik-İstatistik

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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, and 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.

Table of Chapters:
1 Rings and fields
2 Integral domains and polynomials
3 Field extensions
4 Applications to geometry
5 Splitting fields
6 Finite fields
7 The Galois group
8 Equations and groups
9 Some group theory
10 Groups and equations
11 Regular polygons
12 Solutions

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