Study of ABness of commutative noetherian rings
| Project/Area Number |
23840043
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Tokuyama College of Technology |
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Principal Investigator |
ARAYA Tokuji 徳山工業高等専門学校, 一般科目, 准教授 (70613222)
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| Project Period (FY) |
2011 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 可換環論 / ホモロジー / Gorenstein環 / AB環 / ホモロジカル次元 / Cohen-Macaulay環 / 極大Cohen-Macaulay加群 / 次数付環 |
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| Research Abstract |
One of the aim of this study is to define a homological dimension which corresponds to the ABness of commutative noetherian rings, and to research its properties.
We define an "AB-dimension" which is closely related to the ABness of rings. We show that the "Auslander-Reiten conjecture" is true if the AB-dimension is finite.
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Report
(3 results)
Research Products
(46 results)
