| Project/Area Number |
13640030
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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 | Naruto University of Education |
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Principal Investigator |
MARUBAYASHI Hidetoshi Naruto University of Education, Faculty of School Education, Professor, 学校教育学部, 教授 (00034702)
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| Co-Investigator(Kenkyū-buntansha) |
KOBAYASHI Sigeru Naruto University of Education, Faculty of School Education, Associate Professor, 学校教育学部, 助教授 (10195779)
UEDA Akira Shimane University, Faculty of Interdisciplinary Science and Engineering, Associate professor, 総合理工学部, 助教授 (70213345)
SAWABE Masato Naruto University of Education, Faculty of School Education, Assistant, 学校教育学部, 助手 (60346624)
MIYAMOTO Haruo Anan Technical College, Professor, 教授 (50035656)
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| Project Period (FY) |
2001 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2004: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2003: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | Valuation ring / Total valuation / Invariant valuation / Crossed product algebra / Prime ideal / Primary ideal / Ore extension / Martindal quotient ring / Primaty ideal / Ore extensions / Martindale quotient rings / Crossed product / Tamely ramified / valuation ring / prime ideal / primary ideal / total valuation / derivation / division ring / semi-hereditary / 整環 / 歪多項式環 / primary ideals / over rings / 単純環 / total付値環 / duo rings |
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| Research Abstract |
For 2001-2004, we have studied the following four projects which are all concerned with non-commutative valuation rings :
1.We gave a necessary and sufficient conditions for a Dubrovin valuation ring to be fully bounded by using the concept of the prime segments.
2.Martindale quotient rings of Dubrovin valuation rings are determined in terms of the localizations.
3.We have studied non-commutative valuation rings of Ore extensions and found out several important non-commutative valuation rings of Ore extensions.
4.Let G be a totally ordered group and let V be a total valuation ring. We have studied non-commutative valuation rings of the crossed product algebra V G by the graded theoretical methods.
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