2013 Fiscal Year Final Research Report
Study of noncommutative Gorenstein rings
| Project/Area Number |
23540040
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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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| Research Field |
Algebra
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
NISHIDA Kenji 信州大学, 理学部, 教授 (70125392)
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| Research Collaborator |
KOGA Hirotaka 筑波大学, 数理物質系, 特別研究員PD (30736723)
KAMEYAMA Noritsugu 信州大学, 大学院・総合工学系研究科, D3
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| Project Period (FY) |
2011 – 2013
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| Keywords | 非可換ゴレンシュタイン環 |
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| Research Abstract |
First, generalizing the notion of Gorenstein dimension for finitely generated modules over Noetherian rings, we introduced the notion of weak Gorenstein dimension for finitely presented modules over coherent rings. Next, we showed that for a coherent ring, if both the minimal cogenerator for left modules and that for right modules have finite flat dimension then they coincide, and that both the minimal cogenerator for left modules and that for right modules have finite flat dimension if and only if every finitely presented right module has a bounded weak Gorenstein dimension.
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