| Project/Area Number |
23540053
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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 | Saga University |
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Principal Investigator |
TERAI Naoki 佐賀大学, 文化教育学部, 教授 (90259862)
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| Co-Investigator(Kenkyū-buntansha) |
UEHARA Tsuyoshi 佐賀大学, 工学系研究科, 教授 (80093970)
ICHIKAWA Takashi 佐賀大学, 工学系研究科, 教授 (20201923)
MIYAZAKI Chikashi 佐賀大学, 工学系研究科, 教授 (90229831)
KAWAI Shigeo 佐賀大学, 文化教育学部, 教授 (30186043)
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| Co-Investigator(Renkei-kenkyūsha) |
YOSHIDA Kenichi 日本大学, 文理学部, 教授 (80240802)
YANAGAWA Kouji 関西大学, 工学部, 准教授 (40283006)
KIMURA Kyouko 静岡大学, 大学院・理学研究科, 助教 (60572633)
MURAI Satoshi 山口大学, 理学部, 講師 (90570804)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | Stanley-Reisner ideal / minimal free resolution / arithmetical rank / Stanley-Reisner イデアル / 算術階数 / 極小自由分解 / Ｓｔａｎｌｅｙ－Ｒｅｉｓｎｅｒ イデアル |
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| Research Abstract |
We studied the arithmetical rank of Stanly-Reisner ideals, which are squarefree monomial ideals in a polynomial ring. It is known that the arithmetical rank of a Stanley-Reisner ideal is greater than or equal to the projective dimension of the Stanley-Reisner ring, which is the length of the minimal free resolutions of the quotient ring. As for the edge ideal of a forest, Barile conjectures that these numbers will be coincident. We proved it. As for a Gorenstein Stanly-Reisner ideal of height three, we proved that its arithmetical rank is equal to the projective dimension of the Stanly-Reisner ring, too.
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