2006 Fiscal Year Final Research Report Summary
| Project/Area Number |
15540027
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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 | Osaka Kyoiku University |
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Principal Investigator |
BABA Yoshitomo Osaka Kyoiku University, Faculty of Education, Associate Professor, 教育学部, 助教授 (10201724)
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| Co-Investigator(Kenkyū-buntansha) |
KITAMURA Kazuo Osaka Kyoku University, Department of Education, Professor, 教育学部, 教授 (30030381)
UNO Katsuhiro Osaka Kyoku University, Department of Education, Professor, 教育学部, 教授 (70176717)
OSHIRO Kiyoichi Yamaguchi University, Graduate school of Science and Engineering, Professor, 理学部, 教授 (90034727)
YOSHIMURA Hiroshi Yamaguchi University, Graduate school of Science and Engineering, Associate Professor, 理学部, 助教授 (00182824)
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| Project Period (FY) |
2003 – 2006
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| Keywords | ring / R-module / Morita Self-duality / Harada ring / Nakayama ring |
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| Research Abstract |
In the theory of artinian rings, quasi-Frobenius rings ( QF-rings) and Nakayama rings (generalized uniserial rings) are important classical artinian rings. And, in the early 1980s, Manabu Harada found a new class of artinian rings which contain QF-rings and Nakayama rings. Now these new artinian rings are called Harada rings and the study of QF-rings and Nakayama ring from the point of view of Harada rings is very important.
It is well known that QF-rings and Nakayama rings have the Morita self-dualities. But recently it was showed that Harada rings do not have the Morita self-dialities in general. Our first aim is to give answers the question: What kind of Harada rings have the Morita self-dualities. To be specific, we study Harada rings of a component type. The class of Harada rings of a component type contains the class of Nakayama rings, and Nakayama rings are well characterized as a special kind of Harada rings of a component type. In addition, Harada rings of a component type have the Morita weakly symmetric self-dualities.
In [Y. Baba and K. Oshiro: On a theorem of Fuller, Journal of Algebra 154 (1994), 86-94], we study the famous Fuller's theorem which characterizes projective injective modules over artinian rings. This reseach is further studied by T. Sumioka, M. Hoshino, and M. Morimoto. On the other hand, in [Y. Baba: Injectivity of quasi-projective modules, projectivit.y of quasi-injective modules, and projective cover of injective modules, Journal of Algebra 155 (1994), 415--434], we characterized quasi-injective projective modules and quasi-projective injective modules. From this point of view, we studied the above Fuller's Theorem again.
"In addition to these studies, we write a lecture note titled ""Classical artinian rings and related topics"" which includes the above results and further umpublished results. This book will be published in several years"
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Research Products
(11 results)
