2012 Fiscal Year Final Research Report
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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| 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 |
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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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