A study on the structure of complexes of modules
| Project/Area Number |
15K17514
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Fukuoka University of Education |
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Principal Investigator |
OKAZAKI Ryota 福岡教育大学, 教育学部, 准教授 (20624109)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | アフィン有向マトロイド / 有界複体 / 極小次数付き自由分解 / 次数付き自由分解 / 有限次数付き自由分解 / 有向マトロイド / 組合せ論的可換代数 |
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| Outline of Final Research Achievements |
This research has revealed that if the bounded complex X of an affine oriented matroid M is Cohen-Macaulay, then X and the simplicial complex Δ associated with the affine oriented matroid ideal of M are ``homologically'' closed balls. In addition, I have discovered a ``direct'' way to construct a graded free resolution of a finitely generated graded module over a polynomial ring over a field.
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| Academic Significance and Societal Importance of the Research Achievements |
アフィン有向マトロイドに関する成果は，有界複体 X がコーエン＝マコーレーならば X は閉球体であることを窺わせ，X. Dong 氏により肯定的に解決された Zaslavsky 予想の主張がより広いクラスでも成立することを示唆するものである．
加群 M の自由分解は，M の代数的性質を調べる為の重要な概念であり，本研究で得られた自由分解の構成法は多項式環上の次数付き加群に関する研究への寄与が期待できる．
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Report
(5 results)
Research Products
(6 results)
