Science Fair Project Encyclopedia
Galois extension
In mathematics, a Galois extension is a field extension that has a Galois group. A fundamental result of Galois theory characterises these extensions: a finite extension of fields L/K is a Galois extension if and only if it is both a normal extension and a separable extension.
This criterion can be used in practice to show that extensions have Galois groups. It states, in more concrete terms, that L is built up from K as a compositum of a number of splitting fields of separable polynomials.
There is also the result of Emil Artin that starts with L given. If G is a finite group of automorphisms of L, then the fixed field K of G is such that L/K is a Galois extension.
09-23-2007 01:00:40
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details