| Project/Area Number |
17K05202
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 |
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| Co-Investigator(Kenkyū-buntansha) |
小池 寿俊 沖縄工業高等専門学校, 総合科学科, 教授 (20225337)
倉富 要輔 山口大学, 大学院創成科学研究科, 准教授 (60370045)
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| Project Period (FY) |
2017-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 代数学 / 環論 / 原田環 / 中山環 / ＱＦ環 / アルチン環 |
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| Outline of Final Research Achievements |
Research on Harada rings has been actively conducted since around 1979, and the results are included in the lecture notes "Classical artinian rings and related topics", World Scientific Publishing (2009), co-authored by the principal investigator and Professor Emeritus Kiyoichi Oshiro of Yamaguchi University. However, most of the research has focused on one-sided Harada rings, and this research is the first to study the structure of two-sided Harada rings. We began by redefining one-sided Harada rings using new concepts, and succeeded in characterizing them and finding a procedure for constructing a general two-sided Harada ring that is not a Nakayama ring from a certain QF ring.
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| Academic Significance and Societal Importance of the Research Achievements |
原田環の40年以上に渡るこれまでの研究で、この環が古典的アルチン環である中山環やＱＦ環にならぶ優れた性質をもったアルチン環であることが明らかになっている。そして本研究で、両側原田環が初めて本格的に研究され、その右原田性と左原田性の結びつきが明らかになり、中山環ではない一般的な両側原田環の構造が明らかになったことにより、今後それを用いての両側原田環の研究が本格化すると同時に、中山環やＱＦ環等の古典的アルチン環を、片側原田環より精緻に、両側原田環の構造論の視点で研究し直すことが可能になった。
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