Development of local ring theory actively using the theory of Hilbert functions
| Project/Area Number |
18K03241
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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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| Review Section |
Basic Section 11010:Algebra-related
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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) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 可換環論 / 局所環 / 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 / 巴系イデアル |
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| Outline of Final Research Achievements |
The goal of this research project is to develop commutative algebra, a branch of algebra. In particular, I have made new developments in local ring theory by actively using the theory of Hilbert functions of local rings.
In this research, I mainly started to clarify the structure of the associated graded rings and Rees algebras by the first and second Hilbert coefficients. Specifically, I give a new class of structures of associated graded rings by the first and second normal Hilbert coefficients of m-primary ideals in analytically unramified Cohen-Macaulay local rings. These research results were carried out as international joint research with three researchers, and have already been published as two peer-reviewed international papers.
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| Academic Significance and Societal Importance of the Research Achievements |
研究代表者がこれまでに培ってきたSally加群の理論を発展させ、それらを応用することで、これまで解明が困難とされてきたイデアルの正規フィルトレーションの構造の制御が可能となり、第1および第2正規ヒルベルト函数に関する新たな理論を与えることが可能となった。さらに、本研究で築き上げた技術と知見は、今後の局所環のヒルベルト函数の挙動研究における活用も期待出来る。
また、本研究が3カ国の共同研究者との国際共同研究として発展し、一定の成果を残せたことも本研究実施の意義の一つであると考えられる。
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Report
(6 results)
Research Products
(33 results)
