Integral bases of dihedral numberfields. I

Ledermann, Walter and van der Ploeg, Carol (1985) Integral bases of dihedral numberfields. I. Journal of the Australian Mathematical Society (Series A), 38 (3). pp. 351-371. ISSN 1446-7887

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A dihedral number field is a non-normal quartic field K which possesses a quadratic subfield k. That is, for some integer α of k. Integral bases of these fields were known by Sommer (1907), but the form in which they were known was of little use for computational purposes. In this paper we construct integral bases of those dihedral fields with quadratic subfield of the form , d 1 (mod 8), for which only rational quantities need be determined. Although the general theory may easily be generalized to the case d ≡ 1 (mod 8), the actual determination of integral bases in this case is left to a later paper.

Item Type: Article
Schools and Departments: School of Business, Management and Economics > Business and Management
Subjects: Q Science > QA Mathematics > QA0150 Algebra. Including machine theory, game theory
Depositing User: Carol Alexander
Date Deposited: 26 Sep 2012 08:21
Last Modified: 27 Sep 2012 07:50
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