| 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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| Co-Investigator(Kenkyū-buntansha) |
内藤 浩忠 香川大学, 教育学部, 教授 (00180224)
相羽 明 茨城大学, 理学部, 准教授 (90202457)
高橋 浩樹 徳島大学, 大学院・ソシオテクノサイエンス研究部, 准教授 (90291476)
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| Project Period (FY) |
2007 – 2010
|
| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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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 / 正規底 / 正規整数底 / 虚2次体 / Hilbert-Speiser / Stickelberger / Hilbert-Speiser number field |
|---|
| 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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