Study of polynomial fibre rings
Project/Area Number |
16K05096
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | University of Fukui |
Principal Investigator |
Onoda Nobuharu 福井大学, 学術研究院工学系部門, 教授 (40169347)
|
Project Period (FY) |
2016-04-01 – 2020-03-31
|
Project Status |
Completed (Fiscal Year 2019)
|
Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | 可換環論 / アフィン代数幾何学 / 国際研究者交流 / インド / 代数学 / 多項式環 |
Outline of Final Research Achievements |
Some results are obtained regarding polynomial fibre rings which are important both in commutative algebra and affine algebraic geometry. In particular, sufficient conditions are given for an algebra to be Noetherian over a two dimensional complete regular local ring, and examples are constructed to show the necessity of the conditions. Moreover, isomorphism classes are studied for algebras generated by idempotents over a commutative ring. The uniqueness of the isomorphism class is proved for the case where the number of primitive idempotents is finite, and a theorem is given for the case where the number of primitive idempotents is countably infinite.
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Academic Significance and Societal Importance of the Research Achievements |
アフィン代数幾何学に関連する可換環論は,国内外に多くの研究者がいて,近年,急速に研究が進み,関連する研究集会も盛んに開催されている。アフィンファイブレーションはその主要な研究テーマの一つであり,未解明の問題も多い。本研究はその進展に資するものであり,また,インドの研究者3名を海外共同研究者に加えた国際共同研究として,国際協調にも貢献するものである。
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Report
(5 results)
Research Products
(9 results)