| Project/Area Number |
63540039
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | Kyoto Institute of Technology |
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Principal Investigator |
KAWADA Yutaka Kyoto Institute of Technology, Faculty of Engineering and Design, Professor, 工芸学部, 教授 (50027744)
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| Co-Investigator(Kenkyū-buntansha) |
OKURA Hiroyuki Kyoto Institute of Technology, Faculty of Engineering and Design, Associate Prof, 工芸学部, 助教授 (80135649)
MAITANI Fumio Kyoto Institute of Technology, Faculty of Engineering and Design, Associate Prof, 工芸学部, 助教授 (10029340)
NAKAOKA Akira Kyoto Institute of Technology, Faculty of Engineering and Design, Professor, 工芸学部, 教授 (90027920)
HAMADA Yusaku Kyoto Institute of Technology, Faculty of Engineering and Design, Professor, 工芸学部, 教授 (90027764)
SAINOUCHI Yoshikazu Kyoto Institute of Technology, Faculty of Engineering and Design, Professor, 工芸学部, 教授 (00027757)
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| Project Period (FY) |
1988 – 1989
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| Project Status |
Completed (Fiscal Year 1989)
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| Budget Amount *help |
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1989: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1988: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | mod_PA / Transpose / Finite representation type / m.s.s. (minimal spanning system) / Fit matrix theory / fit matrix theory / modpA / 表現順馳型(tamc type) / 極小生成系(m・s・s) / mod_pA / A-R系列 / ディンキン図形 / 表現有限型 / A-R-グラフ |
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| Research Abstract |
The purpose of this research project is to study representation theory of Artinian rings (of finite representation type). For the representation of finite-dimensional algebras over a field there were discovered various methods. But these methods can not always apply to our case. So we had to seek a new method.
We first investigate Auslander-Bridger's duality over a semiperfect ring A. To clarify the content of the duality we shall adopt a restricted matrix theory over A, which is called the fit matrix theory over A, and define a relation matrix R for a module M, non-projective and finitely presented. Then, by means of R, we can succeed in a characterization for M to be in mod_p A, in a framework of the fit matrix theory over A.
Grant-in-Aid for Scientific Research (C) has enabled us to cover the travel expenses to participate in the symposia, seminars, formal or informal meetings in related topics and fields.
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