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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 5
Simple Extensions
The basic building block of field theory is the simple field extension. Here one new
element α is adjoined to a given subfield K of C, along with all rational expressions in
that element over K. Any finitely generated extension can be obtained by a sequence
of simple extensions, so the structure of a simple extension provides vital information
about all of the extensions that we shall encounter.
We first classify simple extensions into two very different kinds: transcendental
and algebraic. If the new element α satisfies a polynomial equation over K, then
the extension is algebraic; if not, it is transcendental. Up to isomorphism, ...
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Publisher Resources

ISBN: 9781482245837