GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS

Yıl 2007, Cilt: 2 Sayı: 2, 100 - 105, 01.12.2007

Patrik Lundström

Öz

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.

Anahtar Kelimeler

Galois theory, normal basis, self-dual basis