2023 Fiscal Year Final Research Report
Study on relationship among ring theoretic invariants for non Cohen-Macaulay rings
| Project/Area Number |
20K03550
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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 | Kitami Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | エッジイデアル / Stanley-Reisner環 / 次元 / Castelnuovo-Mumford正則度 / 余次元 / マッチング数 / 最小マッチング数 / 誘導マッチング数 |
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| Outline of Final Research Achievements |
For quotient rings of polynomial rings by edge ideals associated with finite simple graphs, we found some relationships between ring-theoretic invariants (dimension, depth, the degree of h-polynomials, Castelnuovo-Mumford regularity and codimension) and graph-theoretic invariants (matching number, minimum matching number, induced matching number, the number of vertices and the number of edges).
Moreover, wee also found an inequality for dimension, Castelnuovo-Mumford regularity and Cohen-Macaulay type of Cohen-Macaulay Stanley-Reisner rings.
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| Free Research Field |
可換環論
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| Academic Significance and Societal Importance of the Research Achievements |
エッジイデアルに関する一連の研究において、グラフ理論に関するいくつかの研究成果を用いた。またその逆に、純粋なグラフ理論の問題を解決し、それを応用してエッジイデアルについての研究成果が出せたこともあった。両分野の結びつきの強さを知らしめるような結果が出せたことに意義を感じる。
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