2015 Fiscal Year Final Research Report
The integrated study of orders and valuation rings
| Project/Area Number |
24540058
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokushima Bunri University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
Ueda Akira 島根大学, 総合理工学研究科(研究院), 教授 (70213345)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 環論 / イデアル / 極大整環 / 付値環 / 遺伝的環 |
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| Outline of Final Research Achievements |
We study orders and valuation rings. About order theory, ① we give the necessary and sufficient conditions for the ring of Morita contexts to be maximal orders in terms of modules theory.② we obtain that the necessary and sufficient conditions for skew polynomial rings and differential polynomial rings to be generalized Asano rings. ③we completely describe the structure of projective ideals in skew polynomial rings over hereditary rings, which leads us to find a new class of rings being called "generalized hereditary rings".
About the study of valuation rings,④we study prime ideals in graded extensions for crossed product algebras.
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| Free Research Field |
数学
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