2004 Fiscal Year Final Research Report Summary
Synthetic Study of Prufer Orders and Semi-hereditary Orders
| 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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| Keywords | Valuation ring / Total valuation / Invariant valuation / Crossed product algebra / Prime ideal / Primary ideal / Ore extension / Martindal quotient ring |
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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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Research Products
(20 results)
