Hilbert function of local rings
| Project/Area Number |
15K04820
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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 | Yamaguchi University |
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Principal Investigator |
Ozeki Kazuho 山口大学, 大学院創成科学研究科, 准教授 (70445849)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | ヒルベルト函数 / ヒルベルト係数 / Rees代数 / 随伴次数環 / Sally加群 / コーエン・マコ―レイ局所環 / 随伴次数間 / Cohen-Macaulay環 / 可換環論 / 巴系イデアル |
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| Outline of Final Research Achievements |
The purpose of this research is to explore the behavior of the Hilbert functions of ideals in Cohen-Macaulay local rings.
I explored the relationship between the first Hilbert coefficient and the structure of the associated graded ring of integrally closed ideals in a Cohen-Macaulay local ring.
I also gave a characterization for the almost minimal value of the first Hilbert coefficient in the case of the normal filtration in an analytically unramified Cohen-Macaulay local ring. I strongly used some structure theorems of Sally modules in these results.
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Report
(4 results)
Research Products
(19 results)
