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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 12
The Galois Correspondence
We are at last in a position to establish the fundamental properties of the Galois
correspondence between a field extension and its Galois group. Most of the work has
already been done, and all that remains is to put the pieces together.
12.1 The Fundamental Theorem of Galois Theory
Let us recall a few points of notation from Chapter 8. Let L : K be a field extension
in C with Galois group G, which consists of all K-automorphisms of L. Let F be the
set of intermediate fields, that is, subfields M such that K M L, and let G be the
set of all subgroups H of G. We have defined two maps
: F G
: G F
as follows: if
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Publisher Resources

ISBN: 9781482245837