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Filtered noetherian rings having homological finiteness

Research Project

Project/Area Number 21540035
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

NISHIDA Kenji  信州大学, 理学部, 教授 (70125392)

Project Period (FY) 2009 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywordsネータ多元環 / フィルター環 / フィルター加群 / マトリス双対 / アウスランダー正則 / アウスランダーゴレンステイン / ホモロジー代数学 / G-射影加群 / ゴレンステイン射影的 / シジジー・余シジジー / ゴレンステイン多元環 / ゴレステイン次元 / 余シジジー / ネータ環 / 単純加群に付随する傾加群 / 変異 / ネータ整環 / 擬コンパクト多元環 / 岩澤代数 / 局所コホモロジー / 局所双対
Research Abstract

We define the topology of a filtered pseudo-compact algebra induced from a filter of a ring. Then we can use algebraic method to study a filtered pseudo-compact algebra. By defining toplogy of filtered pseudo compact algebra induced from the filter, we give filtered pseudo compact algebra pury algebraic definition of filtered pseudo compact algebra. That is, suppose that the filter is induced from the maximum idal then filtered pseudo compact algebra is noetherian and semiperfect. The category of all finitely generated modules over noetherian semiperfect ring has good property, i.e. all the modules in it has a projective cover. This fact is highly connected to approximation theory. Hence filtered pseudo compact algebra is expected to the representation theory of non-commutative noetherian algebras.

Report

(5 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (3 results)

All 2011 2009

All Presentation (3 results)

  • [Presentation] 整環の表現と傾加群2011

    • Author(s)
      西田憲司
    • Organizer
      56回代数学シンポジウム
    • Place of Presentation
      岡山大学
    • Year and Date
      2011-08-09
    • Related Report
      2012 Final Research Report
  • [Presentation] 整環の表現と傾加群2011

    • Author(s)
      西田憲司
    • Organizer
      第56回代数学シンポジウム
    • Place of Presentation
      岡山大学環境理工学部(招待講演)
    • Year and Date
      2011-08-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] フィルターネータ環上のマトリス双対2009

    • Author(s)
      亀山統胤、西田憲司
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2012 Final Research Report 2009 Annual Research Report

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Published: 2009-04-01   Modified: 2019-07-29  

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