| Project/Area Number |
21540041
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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 |
KUTAMI Mamoru 山口大学, 大学院・理工学研究科, 教授教授 (80034734)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIMURA Hiroshi 山口大学, 大学院・理工学研究科, 准教授 (00182824)
KIKUMASA Isao 山口大学, 大学院・理工学研究科, 准教授 (70234200)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 環論・加群論 / ノイマン正則環 / 比較可能性 / 有限性 / ダイレクト・ファイナイト性 / 射影加群 / 削除問題 / イノマン正則環 / 一般Almost比較可能性 / S-比較可能性 / Almost比較可能性 / ダイレクトファイナイト性 |
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| Research Abstract |
The study of von Neumann regular rings was first begun from the study of commutative von Neumann regular rings and the study of continuous von Neumann regular rings which contain self-injective von Neumann regular rings. Recently, the investigation of von Neumann regular rings with comparabilities has been proceeded by many ring theorists. Historically, the main themes for studies of von Neumann regular rings are the investigations of finiteness, characteristics and constructions. In this research, we investigated finiteness, hereditarity to matrix rings, cancellations and constructions on von Neumann regular rings with various comparabilities, to construct the theory of von Neumann regular rings with comparabilities.
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