2017 Fiscal Year Final Research Report
Developement of the theory of non-Gorenstein rings and a study of j-multiplicity
| 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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| Keywords | Almost Gorenstein環 / Gorenstein環 / 系列的Cohen-Macaulay環 / Rees代数 / Arf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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| Free Research Field |
代数学
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