| Project/Area Number |
26400054
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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 | Meiji University |
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Principal Investigator |
Tran Thi Phuong 明治大学, 研究・知財戦略機構, 研究推進員(客員研究員) (00649824)
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| Co-Investigator(Kenkyū-buntansha) |
松岡 直之 明治大学, 理工学部, 専任講師 (80440155)
谷口 直樹 明治大学, 理工学部, 助教 (30782510)
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| Co-Investigator(Renkei-kenkyūsha) |
GOTO Shiro 明治大学, 理工学部, 名誉教授 (50060091)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | Almost Gorenstein環 / Gorenstein環 / 系列的Cohen-Macaulay環 / Rees代数 / Arf環 / 可換環論 / 概ゴレンシュタイン環 / アーフ環 / ゴレンシュタイン環 / コーエン・マコーレー環 / サリー加群 / 正準イデアル / 極小自由分解 / 数値半群環 / 行列式環 / リース代数 / 正規ヒルベルト係数 / 随伴次数環 |
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| Outline of Final Research Achievements |
The purpose of this research is to enrich the theory of one-dimensional almost Gorenstein rings, which was originally studied by Barucci-Froeberg and Goto-Matsuoka-Phuong, and to develop the theory for higher dimension. Among them, we studied the almost Gorenstein property for Rees algebras, determinantal rings, and Arf rings. In parallel, we analyzed the sequentially Cohen-Macaulay property for the Rees algebras in order to make progress the theory of non-Cohen-Macaulay rings and modules.
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