1989 Fiscal Year Final Research Report Summary
Study on Representation Theory
| 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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| Keywords | mod_PA / Transpose / Finite representation type / m.s.s. (minimal spanning system) / Fit matrix theory / fit matrix theory |
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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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