VON NEUMANN REGULAR RINGS WITH COMPARABILITIES

具有可比性的冯诺依曼常规环

• 批准号: 21540041
• 负责人: KUTAMI Mamoru
• 金额: $ 1.58万
• 依托单位: Yamaguchi University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540041/
• 关键词: 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

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.

Von Neumann正则环的研究最早是从交换von Neumann正则环和包含自内射von Neumann正则环的连续von Neumann正则环的研究开始的。最近，许多环理论家对具有可比性的von Neumann正则环进行了研究。从历史上看，von Neumann正则环的研究主题主要是对有限性、特征和结构的研究。本文研究了具有不同可比性的von Neumann正则环上矩阵环的有限性、遗传性、消去性和构造性，从而建立了具有可比性的von Neumann正则环理论。

项目成果

Von Neumann regular rings with generalized almost comparability

具有广义几乎可比性的冯诺依曼正则环

• 发表时间: 2011
• 作者: Maxim;Laurentiu; Saito;Morihiko; Schurmann;Jorg;木村俊一;Mamoru Kutami
• 通讯作者: Mamoru Kutami

Almost comparability and related comparabilities in von Neumann regular rings

冯·诺依曼正则环中的几乎可比性和相关可比性

• 发表时间: 2010
• 期刊: Proceeedings of the 42nd Symposium on Ring Theory and Representation Theory
• 作者: 田端亮;木材俊一;Shun-ichi Kimura;Hideto Asashiba;木村俊一;S. Kimura;Shun-ichi Kimura;木村俊一;木村俊一;木村俊一;浅芝秀人;Mamoru Kutami
• 通讯作者: Mamoru Kutami