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VON NEUMANN REGULAR RINGS WITH COMPARABILITIES

Research Project

Project/Area Number 21540041
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionYamaguchi University

Principal Investigator

KUTAMI Mamoru  山口大学, 大学院・理工学研究科, 教授教授 (80034734)

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)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
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)
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
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.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (10 results)

All 2012 2011 2010 2009 Other

All Journal Article (5 results) (of which Peer Reviewed: 3 results) Presentation (4 results) Remarks (1 results)

  • [Journal Article] Von Neumann regular rings satisfying generalized almost comparability2012

    • Author(s)
      Mamoru Kutami
    • Journal Title

      Advances in Ring Theory, World Scientific Publishers

      Pages: 96-108

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Almost comparability and related comparabilities in von Neumann regular rings2010

    • Author(s)
      Mamoru Kutami
    • Journal Title

      Proceedings of the 42nd Symposium on Ring Theory and Representation Theory

      Pages: 38-45

    • Related Report
      2011 Final Research Report
  • [Journal Article] Almost comparability and related comparabilities in von Neumann regular rings2010

    • Author(s)
      Mamoru Kutami
    • Journal Title

      Proceeedings of the 42nd Symposium on Ring Theory and Representation Theory

      Pages: 38-45

    • Related Report
      2009 Annual Research Report
  • [Journal Article] A construction of local QF rings and its characterization

    • Author(s)
      I. Kikumasa, K. Oshiro, H. Yoshimura
    • Journal Title

      Communications in Algebra

      Volume: (掲載決定)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A construction of local QF rings and its characterization

    • Author(s)
      Isao Kikumasa
    • Journal Title

      Communications in Algebra

      Volume: (掲載決定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Von Neumann regular rings with generalized almost comparability2011

    • Author(s)
      Mamoru Kutami
    • Organizer
      The 6th China-Japan-Korea International Conference on Ring and Module Theory
    • Place of Presentation
      Suwon, South Korea
    • Year and Date
      2011-06-28
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] ある種の多元環の同型について2011

    • Author(s)
      古谷亮輔、菊政勲、吉村浩
    • Organizer
      平成22度日本数学会中国・四国支部例会
    • Place of Presentation
      鳴門地域地場産業振興センター
    • Year and Date
      2011-01-30
    • Related Report
      2011 Final Research Report
  • [Presentation] ある種の多元環の同型について2011

    • Author(s)
      古谷亮輔、菊政勲、吉村浩
    • Organizer
      平成22年度日本数学会中国・四国支部例会
    • Place of Presentation
      鳴門地域地場産業振興センター
    • Year and Date
      2011-01-30
    • Related Report
      2010 Annual Research Report
  • [Presentation] Almost comparability and related comparabilities in von Neumann regular rings2009

    • Author(s)
      久田見守
    • Organizer
      第42回環論および表現論シンポジウム
    • Place of Presentation
      大阪教育大学
    • Year and Date
      2009-10-12
    • Related Report
      2011 Final Research Report 2009 Annual Research Report
  • [Remarks] 環論ホームページ

    • URL

      http://www.cec.yamanashi.ac.jp/.ring/

    • Related Report
      2011 Final Research Report

URL: 

Published: 2009-04-01   Modified: 2016-04-21  

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