Patrik LUNDSTRÖM

11068

GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS

GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS

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,

International Electronic Journal of Algebra-Cover

ISSN: 1306-6048
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2007
Yayıncı: Abdullah HARMANCI

Arşiv

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