| Project/Area Number |
20540035
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Hokkaido University of Education |
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Principal Investigator |
HARIMA Tadahito Hokkaido University of Education, 教育学部, 准教授 (30258313)
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| Co-Investigator(Kenkyū-buntansha) |
WATANABE Junzo 東海大学, 理学部, 教授 (40022727)
WACHI Akihito 北海道教育大学釧路校, 教育学部, 准教授 (30337018)
ISOGAWA Satoru 熊本高等専門学校, 共通教育科, 教授 (80223056)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 完全交叉 / レフシェッツ性 / ジェネリックイニシャルイデアル / 単項式イデアルゴレンスタイン環 / ジョルダン標準形 / 可換環 / ゴレンスタイン環 / リース元 / 単項式イデアル / Rees元 / 強いレフシェッツ性 / ヘッセ行列 / rev-lexイデアル |
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| Research Abstract |
The Lefschetz properties are basic and important properties for Artinian graded algebras. In this research, we studied the Lefschetz properties and generic initial ideals of complete intersections. As a result, we obtained the following. 1. We gave a sharp upper bound on the Betti numbers of Artinian algebras with the k-Lefsctez property and a fixed Hilbert function. 2. We found generic initial ideals of some complete intersections in four variables. 3. The tensor product of strongest Jordan decompositions is again strongest. This is a generalization of the fact which states that the strong Lefschetz property is preserved by tensor product. 4. We gave some examples of Gorenstein algebras not having the weak Lefschetz property.
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