2010 Fiscal Year Final Research Report
Hilbert-Speiser number fields and Stickelberger ideals
| Project/Area Number |
19540005
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Ibaraki University |
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Principal Investigator |
ICHIMURA Humio Ibaraki University, 理学部, 教授 (00203109)
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| Project Period (FY) |
2007 – 2010
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| Keywords | Hilbert-Speiserの定理 / Stickelberger ideal / 整数環 / ideal類群 / 円分体 / 円分岩澤理論 |
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| Research Abstract |
For a fixed prime number p and an integer n, we say that a number field F satisfies the Hilbert-Speiser condition A(p^n) when any abelian extension N/F of exponent dividing p^n has a normal basis with respect to the rings of p-integers. We gave a condition for F to satisfy A(p^n) in terms of a certain Stickelberger ideal.
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