GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS

Authors : Patrik LUNDSTRÖM

Pages : 100-105

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Publication Date : 2007-12-01

Article Type : Research Paper

Abstract :We show, in two different ways, that every finite field extension has a basis with the property that the Galois group of the extension acts faithfully on it. We use this to prove a Galois correspondence theorem for general finite field extensions. We also show that if the characteristic of the base field is different from two and the field extension has a normal closure of odd degree, then the extension has a self-dual basis upon which the Galois group acts faithfully.
Keywords : Galois theory, normal basis, self dual basis