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ID 47191
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Author
Ichimura, Humio
Abstract
We say that a number field F satisfies the condition (H′2m) when any abelian extension of exponent dividing 2m has a normal basis with respect to rings of 2-integers. We say that it satisfies (H′ 2) when it satisfies (H′ 2m) for all m. We give a condition for F to satisfy (H'2m), and show that the imaginary quadratic fields F = Q(√−1) and Q(√−2) satisfy the very strong condition (H′ 2) if the conjecture that h+2m = 1 for all m is valid. Here, h+2m) is the class number of the maximal real abelian field of conductor 2m.
Keywords
Hilbert-Speiser number field
Stickelberger ideal
normal integral basis
Published Date
2012-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume54
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
33
End Page
48
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Copyright©2012 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol54/iss1/2
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