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Galois Theory, 4th Edition
book

Galois Theory, 4th Edition

by Ian Nicholas Stewart
March 2015
Intermediate to advanced content levelIntermediate to advanced
344 pages
10h 18m
English
Chapman and Hall/CRC
Content preview from Galois Theory, 4th Edition
Chapter 4
Field Extensions
Galois’s original theory was couched in terms of polynomials over the complex field.
The modern approach is a consequence of the methods used, starting around 1890
and flourishing in the 1920s and 1930s, to generalise the theory to arbitrary fields.
From this viewpoint the central object of study ceases to be a polynomial, and be-
comes instead a ‘field extension’ related to a polynomial. Every polynomial f over a
field K defines another field L containing K (or at any rate a subfield isomorphic to
K). There are conceptual advantages in setting up the theory from this point of view.
In this chapter we define field extensions (always ...
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Publisher Resources

ISBN: 9781482245837