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Galois Module Structure of Field Extensions
University West, Department of Technology, Mathematics and Computer Science, Division for Mathematics and Sciences. University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0001-6594-7041
2007 (English)In: International Electronic Journal of Algebra, ISSN 1306-6048, E-ISSN 1306-6048, Vol. 2, no 8, p. 100-105Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2007. Vol. 2, no 8, p. 100-105
Keywords [en]
Galois theory, normal basis, self-dual basis
National Category
Algebra and Logic
Research subject
ENGINEERING, Mathematics
Identifiers
URN: urn:nbn:se:hv:diva-118OAI: oai:DiVA.org:hv-118DiVA, id: diva2:211189
Available from: 2009-04-09 Created: 2009-04-09 Last updated: 2020-04-02Bibliographically approved

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Patrik, Lundström

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