2001 Fiscal Year Final Research Report Summary
Research of quasi-Frobenius rings and representation theory
| Project/Area Number |
12640027
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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 | Yamaguchi University |
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Principal Investigator |
YOSHIMURA Hiroshi Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (00182824)
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| Co-Investigator(Kenkyū-buntansha) |
KIKUMASA Isao Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (70234200)
OSHIRO Kiyoichi Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (90034727)
KATAYAMA Hisao Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (00043860)
KIUCHI Isao Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (30271076)
KUTAMI Mamoru Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (80034734)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Ring theory / Quasi-Frobenius rings / Extending modules / Self-duality of rings / Von-Neumann regular rings |
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| Research Abstract |
This research in concerned with quasi-Frobenius rings and their representation theory. Allotting a portion of the project to each investigator, I studied the structures and representations of quasi-Frobenius rings and related rings. Consequently, we obtained the following results.
1. We constructed an algorithm for deciding whether a given factor algebra of a polynomial ring over a field is quasi-Frobenius and implemented the algorithm to computers. By this method, we completely determined the isomorphism classes of commutative quasi-Frobenius algebras with radical cube zero.
2. We determined the condition for extending modules to be closed under finite direct sums and investigated self-duality of Auslander rings of local serial rings.
3. We studied the "Direct Finite" property of modules of von-Neumann regular rings with weak comparability axiom.
4. We also obtained other related results to this research.
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Research Products
(24 results)
