ID | 47191 |
FullText URL | |
Author |
Ichimura, Humio
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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.
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Keywords | Hilbert-Speiser number field
Stickelberger ideal
normal integral basis
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Published Date | 2012-01
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Publication Title |
Mathematical Journal of Okayama University
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Volume | volume54
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Issue | issue1
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Publisher | Department of Mathematics, Faculty of Science, Okayama University
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Start Page | 33
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End Page | 48
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ISSN | 0030-1566
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NCID | AA00723502
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Content Type |
Journal Article
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language |
English
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Copyright Holders | Copyright©2012 by the Editorial Board of Mathematical Journal of Okayama University
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File Version | publisher
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Refereed |
True
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Submission Path | mjou/vol54/iss1/2
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JaLCDOI |