| Project/Area Number |
13640028
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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 |
OSHIRO Kiyoichi Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (90034727)
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| Co-Investigator(Kenkyū-buntansha) |
KIKUMASA Isamu Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (70234200)
YOSHIMURA Hirosi Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (00182824)
KUTAMI Mamoru Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (80034734)
KADO Jiro Osaka City University, Faculty of Science, Lecture, 理学部, 講師 (10117939)
IIYORI Nobuyasu Yamaguchi University, Education, Associate Professor, 教育学部, 助教授 (00241779)
木内 功 山口大学, 理学部, 助教授 (30271076)
片山 寿男 山口大学, 理学部, 教授 (00043860)
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| Project Period (FY) |
2001 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2001: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | OF-ring / Nakayama ring / Harada ring / Skew-Matrix ring / extending module / lifting module / generalized relative injectivity / generalized relative projectivity / Artinian ring / Quasi-Frobenius ring / sjkew-matrix ring / Nakayama-permutation / Nakayama -automorphism / Artin環 / QF-環 / Nakayama環 / CS-加群 / Harada環 / Nakayama置換 / Nakayama自己同型 |
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| Research Abstract |
(1) head investigator Oshiro has been extensively studied on Quasi-Frobeniu ring and Nakayama ring as applications of Harada rings (which was introduced by Oshiro). In research [1], Oshiro gave a survey on Harada ring and applications, most of which is due to Oshiro
(2) In [2],[3], we studied the open problem when direct sum of extending modules are extending modules. We readied to a situation that this problem should be studied by considering two types. In this paper, we completely solved on one type, by introducing generalized relative injectivity. Recently, this generalized relative injectivity is called "objectivity" (Oshiro injectivity)
(3)Dr Kuratomi is a student of the headinvestigator. In [6], he studied dual result of [3] and gave a very nice result.
(4) Oshiro [1],[2],[3], Baba [4], Koike [5], Kuratomi [6] are important papers for this research project. In particular, in [5], Koike discovered an exsample of a Quasi-Frobenius ring without Nakayama automorphism. This result is a very important and , in some sense, this paper completes the headinvestigator's many years study on Artinian rings.
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