Filtered noetherian rings having homological finiteness
| Project/Area Number |
21540035
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Shinshu University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | ネータ多元環 / フィルター環 / フィルター加群 / マトリス双対 / アウスランダー正則 / アウスランダーゴレンステイン / ホモロジー代数学 / G-射影加群 / ゴレンステイン射影的 / シジジー・余シジジー / ゴレンステイン多元環 / ゴレステイン次元 / 余シジジー / ネータ環 / 単純加群に付随する傾加群 / 変異 / ネータ整環 / 擬コンパクト多元環 / 岩澤代数 / 局所コホモロジー / 局所双対 |
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| Research Abstract |
We define the topology of a filtered pseudo-compact algebra induced from a filter of a ring. Then we can use algebraic method to study a filtered pseudo-compact algebra. By defining toplogy of filtered pseudo compact algebra induced from the filter, we give filtered pseudo compact algebra pury algebraic definition of filtered pseudo compact algebra. That is, suppose that the filter is induced from the maximum idal then filtered pseudo compact algebra is noetherian and semiperfect. The category of all finitely generated modules over noetherian semiperfect ring has good property, i.e. all the modules in it has a projective cover. This fact is highly connected to approximation theory. Hence filtered pseudo compact algebra is expected to the representation theory of non-commutative noetherian algebras.
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Report
(5 results)
Research Products
(3 results)
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[Presentation] 整環の表現と傾加群2011
Author(s)
西田憲司
Organizer
第56回代数学シンポジウム
Place of Presentation
岡山大学環境理工学部(招待講演)
Year and Date
2011-08-09
Related Report
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