2011 Fiscal Year Final Research Report
Research on the Hilbert functions in commutative algebra
| Project/Area Number |
22740026
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Meiji University |
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Principal Investigator |
OZEKI Kazuho 明治大学, 研究・知財戦略機構, ポスト・ドクター (70445849)
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| Project Period (FY) |
2010 – 2011
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| Keywords | 可換環論 / ヒルベルト函数 / ヒルベルト係数 / コーエンマコーレイ環 / ブックスバウム環 / FLCを持つ環 |
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| Research Abstract |
The purpose of this research is to explore the behavior of the Hilbert functions of m-primary ideals in a commutative Noetherian local ring A with the maximal ideal m. The representative of this research gave the following results.
1.Research on the first Hilbert coefficients of m-primary ideals
The purpose of this research is to study the equality on the first Hilbert coefficients of m-primary ideals given in Elias and Valla, without assuming that the base local ring(A, m) is Cohen-Macaulay. It is related to the Buchsbaumness of the associated graded ring of m-primary ideals.
2.Research on the Hilbert coefficients of parameter ideals
This research shows that the Hilbert coefficients of parameter ideals have uniform bounds if and only if the base local ring A has finitely generated local cohomology modules. The uniform bounds are huge ; the sharp bound for the second Hilbert coefficient in the case where the base local ring has finitely generated local cohomology modules.
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