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GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS

Year 2007, Volume: 2 Issue: 2, 100 - 105, 01.12.2007

Patrik Lundström

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

Year 2007, Volume: 2 Issue: 2, 100 - 105, 01.12.2007

Patrik Lundström

Abstract

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Details

Other ID JA29NB35BU
Journal Section Articles
Authors

Patrik Lundström This is me

Publication Date December 1, 2007
Published in Issue Year 2007 Volume: 2 Issue: 2

Cite

APA Lundström, P. (2007). GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS. International Electronic Journal of Algebra, 2(2), 100-105.
AMA Lundström P. GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS. IEJA. December 2007;2(2):100-105.
Chicago Lundström, Patrik. “GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS”. International Electronic Journal of Algebra 2, no. 2 (December 2007): 100-105.
EndNote Lundström P (December 1, 2007) GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS. International Electronic Journal of Algebra 2 2 100–105.
IEEE P. Lundström, “GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS”, IEJA, vol. 2, no. 2, pp. 100–105, 2007.
ISNAD Lundström, Patrik. “GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS”. International Electronic Journal of Algebra 2/2 (December 2007), 100-105.
JAMA Lundström P. GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS. IEJA. 2007;2:100–105.
MLA Lundström, Patrik. “GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS”. International Electronic Journal of Algebra, vol. 2, no. 2, 2007, pp. 100-5.
Vancouver Lundström P. GALOIS MODULE STRUCTURE OF FIELD EXTENSIONS. IEJA. 2007;2(2):100-5.