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Integral bases of dihedral numberfields. I

journal contribution
posted on 2023-06-08, 12:23 authored by Walter Ledermann, Carol AlexanderCarol Alexander
A dihedral number field is a non-normal quartic field K which possesses a quadratic subfield k. That is, for some integer a 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.

History

Publication status

  • Published

Journal

Journal of the Australian Mathematical Society (Series A)

ISSN

1446-7887

Publisher

Cambridge University Press

Issue

3

Volume

38

Page range

351-371

Department affiliated with

  • Business and Management Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-09-26

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