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Synthetical study of ring and representation Theory based on Quasi-Frobenius rings

Research Project

Project/Area Number 18340011
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

OSHIRO Kiyoichi  Yamaguchi University, 名誉教授 (90034727)

Co-Investigator(Kenkyū-buntansha) YOSHIMURA Hiroshi  山口大学, 大学院・理工学研究科, 准教授 (00182824)
IIYORI Nobuo  山口大学, 教育学部, 准教授 (00241779)
KOSHITANI Shigeo  千葉大学, 理学部, 教授 (30125926)
NISHIDA Kenji  信州大学, 理学部, 教授 (70125392)
HANAKI Akihide  信州大学, 理学部, 准教授 (50262647)
KOIKE Kazutoshi  沖縄工業高等専門学校, 一般科, 教授 (20225337)
久田見 守  山口大学, 大学院・理工学研究科, 教授 (80034734)
菊政 勲  山口大学, 大学院・理工学研究科, 准教授 (70234200)
河田 成人  大阪市立大学, 理学部, 准教授 (50195103)
Co-Investigator(Renkei-kenkyūsha) KUTAMI Mamoru  山口大学, 大学院・理工学研究科, 教授 (80034734)
KIKUMASA Isao  山口大学, 大学院・理工学研究科, 准教授 (70234200)
YAMAGTA Kunio  東京農業大学, 工学部, 教授 (60015849)
SATOU Masahisa  山梨大学, 医学工学総合研究部, 教授 (30143952)
ASASHIBA Hideto  静岡大学, 理学部, 教授 (70175165)
KAWATA Shigeto  大阪市立大学, 理学・研究科, 准教授 (50195103)
BABA Yositomo  大阪教育大学, 教育学部, 教授 (10201724)
MARUBAYASI Hidetoshi  徳島文理大学, 工学部, 教授 (00034702)
Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥12,340,000 (Direct Cost: ¥10,300,000、Indirect Cost: ¥2,040,000)
Fiscal Year 2008: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2007: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2006: ¥3,500,000 (Direct Cost: ¥3,500,000)
Keywordsアルチン環 / Quasi-Frobenius 環 / Nakayama環 / Faith予想 / 環論 / Quasi-Frobenius rings / Nakayama rings / skew matrix rings / Harada rings / Faith conjecture / serial group algebra / 環論・表現論 / Quasi Frobenius ringa / Nakayama ring / skew-matrix ring / Harada ring / Moritaduality / Quasi-Frobenius ring / Morita duality
Research Abstract

研究代表者のHarada 環の構造論、Nakayama環のclassification, skew matrix ringの基礎理論を広範な応用を視野に入れて研究し、より進化した形の理論に仕上げることができた。これらの理論を基盤にして分担者の馬場との共同で"Classical Artinian Rings and RelatedTopics"なる専門書を作成した。この本は2009 年にシンガポールのWSPC社から出版されることになった。この本の完成により本研究も研究代表者の長年の研究も完結をみた

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (35 results)

All 2009 2008 2007 2006 Other

All Journal Article (21 results) (of which Peer Reviewed: 6 results) Presentation (9 results) Remarks (5 results)

  • [Journal Article] Skew Matrix rings2009

    • Author(s)
      大城 紀代市, 他2人
    • Journal Title

      Proceedings of the Fifth China-Japan-Korea Conference, Ring Theory, 2007

      Pages: 248-271

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Morita Duality and Recent Revedopment2009

    • Author(s)
      小池 寿俊
    • Journal Title

      Proceeding of the fifth China-Japan-Korea Cponference, Ring Theory, 2007

      Pages: 101-115

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Iwasawa Algebras, closed products and filtered rings2009

    • Author(s)
      西田 憲司
    • Journal Title

      Prooceedings of the 4lst Symposium on Ring Theory and Representation Theory

      Pages: 67-67

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Iwasawa algebras, crossed products and filtered rings2008

    • Author(s)
      西田憲司
    • Journal Title

      Proceedings of the 40th Symposium on Ring Theory and Representation Theory

      Pages: 12-17

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Skew-Matrix Rings and Applications to QF-Rings2008

    • Author(s)
      永富能久、大城紀代市、宇原昌彦、山浦広太
    • Journal Title

      Proceedings of the Fifth China-Japan-Korea Conference on Ring Theory 2007

      Pages: 101-115

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Manabu Harada- The man and his Work2008

    • Author(s)
      大城紀代市
    • Journal Title

      Proceedings of the Fifth China-Japan-Korea Conference on Ring Theory 2007

      Pages: 101-115

    • Related Report
      2008 Final Research Report
  • [Journal Article] Morita Duality and Recent Development2008

    • Author(s)
      小池寿俊
    • Journal Title

      Proceedings of the Fifth China-Japan-Korea Conference on Ring Theory 2007

      Pages: 101-115

    • Related Report
      2008 Final Research Report
  • [Journal Article] Broue's abelian defect group conjecture holds for the Janko simple group J42008

    • Author(s)
      越谷 重央, 他2人
    • Journal Title

      Journal of Pure and Applied Algebra 212

      Pages: 1438-1456

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On colocal pairs2007

    • Journal Title

      Proceedings of the 40^<th> Symposium on Ring Theory and Representation Theory

      Pages: 12-17

    • Related Report
      2008 Final Research Report
  • [Journal Article] Artin 環2007

    • Author(s)
      大城紀代市
    • Journal Title

      研究集会「環論とその周辺」報告集

      Pages: 1-40

    • Related Report
      2008 Final Research Report
  • [Journal Article] Artin環2007

    • Author(s)
      大城 紀代市
    • Journal Title

      「環論とその周辺」報告集

      Pages: 1-39

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A construction of local QRF-rings with Radical cubed zero2007

    • Author(s)
      大城 紀代市 他2人
    • Journal Title

      Proceedings of the 39th Symposium on Ring Theory and Representation Theory

      Pages: 36-44

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Von Neumann regular rings with comparability2006

    • Author(s)
      久田見守
    • Journal Title

      Proceedings of the39th Symposium on Ring Theory and Representation Theory

      Pages: 136-142

    • Related Report
      2008 Final Research Report
  • [Journal Article] Azumaya Conjecture and Harada rings2006

    • Author(s)
      小池寿俊
    • Journal Title

      Proceedings of the 9^<th> Symposium on Ring Theory and Representation Theory

      Pages: 90-95

    • Related Report
      2008 Final Research Report
  • [Journal Article] A construction of local QF-rings with radical cubed zero2006

    • Author(s)
      菊政勲、大城紀代市、吉村浩
    • Journal Title

      zero, Proceedings of the 39^<th> Symposium on Ring Theory and Representation Theory

      Pages: 30-34

    • Related Report
      2008 Final Research Report
  • [Journal Article]2006

    • Author(s)
      小池 寿俊
    • Journal Title

      Journal of Algebra 302

      Pages: 613-645

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On regular rings satisfying weak chain condition2006

    • Author(s)
      久田見 守
    • Journal Title

      Mathematical Journal of Okayama University 48

      Pages: 33-42

    • NAID

      120002309703

    • Related Report
      2006 Annual Research Report
  • [Journal Article] An extension of Watanabe's theorem for the Isaacs-Horimoto-Watanabe corresponding blocks,2006

    • Author(s)
      越谷 重夫 他一人
    • Journal Title

      Journal of Algebra 296

      Pages: 513-524

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On Auslander-Reiten components and Heller lattices for integral group rings2006

    • Author(s)
      河田 成人
    • Journal Title

      Algebr.Represent.Theory 9

      Pages: 513-524

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Isomorphism classes of algebras with radical cube zero II,

    • Author(s)
      大城 紀代市, 他2人
    • Journal Title

      Applied Categorical Structures, Springer to appear. (印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Von Neumann regular rings satisfying weak comparability,

    • Author(s)
      久田見 守
    • Journal Title

      Applied Categorical Structures, Springer, to appear. (印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Iwasawa algebras, crossed products and filtered rings2008

    • Author(s)
      西田憲司
    • Organizer
      第40回環論および表現論研究集会
    • Place of Presentation
      静岡大学
    • Year and Date
      2008-09-05
    • Related Report
      2008 Final Research Report
  • [Presentation] Iwasawa algebras, closed products and filtered rings2008

    • Author(s)
      西田 憲司
    • Organizer
      第41回環論及び表現論研究集会
    • Place of Presentation
      静岡大学理学部
    • Year and Date
      2008-09-05
    • Related Report
      2008 Annual Research Report
  • [Presentation] The Frame QF-subring of Harada Rings2008

    • Author(s)
      大城紀代市
    • Organizer
      Internatinal Conference on Ring and Module Theory
    • Place of Presentation
      Hacette University, Ankara
    • Year and Date
      2008-08-24
    • Related Report
      2008 Final Research Report
  • [Presentation] Morita Duality and Recent Development Recent Development2007

    • Author(s)
      小池寿俊
    • Organizer
      第5回China-Japan-Korea Ring Theory 国際研究集会
    • Place of Presentation
      第5回China-Japan-Korea Ring Theory 国際研究集会
    • Year and Date
      2007-09-14
    • Related Report
      2008 Final Research Report
  • [Presentation] Manabu Harada- The man and his Work2007

    • Author(s)
      大城紀代市
    • Organizer
      第5回China-Japan-Korea Ring Theory 国際研究集会
    • Place of Presentation
      東京オリンピック記念センター
    • Year and Date
      2007-09-12
    • Related Report
      2008 Final Research Report
  • [Presentation] Professor Harada-Person and work2007

    • Author(s)
      大城 紀代市
    • Organizer
      第5回日-中・韓 環論国際研究集会
    • Place of Presentation
      東京オリンピック記念青少年センター
    • Year and Date
      2007-09-12
    • Related Report
      2007 Annual Research Report
  • [Presentation] Azumaya Conjecture and Harada rings2006

    • Author(s)
      小池寿俊
    • Organizer
      第39回環論および表現論研究集会
    • Place of Presentation
      広島大学
    • Year and Date
      2006-09-17
    • Related Report
      2008 Final Research Report
  • [Presentation] A construction of local QF-rings with radical cubed zero2006

    • Author(s)
      大城紀代市
    • Organizer
      第39回環論および表現論研究集会
    • Place of Presentation
      広島大学
    • Year and Date
      2006-09-16
    • Related Report
      2008 Final Research Report
  • [Presentation] Artin 環2006

    • Author(s)
      大城紀代市
    • Organizer
      研究集会「環論とその周辺」
    • Place of Presentation
      名古屋大学
    • Related Report
      2008 Final Research Report
  • [Remarks] 第39回環論および表現論研究集会報告集(200冊)

    • Related Report
      2008 Final Research Report
  • [Remarks] 第40回環論および表現論研究集会報告集(200冊)

    • Related Report
      2008 Final Research Report
  • [Remarks] 第41回環論および表現論研究集会報告集(200冊)

    • Related Report
      2008 Final Research Report
  • [Remarks] 環論と「その周辺」研究集会報告集(200冊)

    • Related Report
      2008 Final Research Report
  • [Remarks] Proceedings of the Fifth China-Japan-Korea Conference on Ring Theory 2007, WSPC 社(110冊)

    • Related Report
      2008 Final Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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