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Study on Artinian rings with priority given to Quasi-Frobenius rings

Research Project

Project/Area Number 13640028
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

OSHIRO Kiyoichi  Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (90034727)

Co-Investigator(Kenkyū-buntansha) KIKUMASA Isamu  Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (70234200)
YOSHIMURA Hirosi  Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (00182824)
KUTAMI Mamoru  Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (80034734)
KADO Jiro  Osaka City University, Faculty of Science, Lecture, 理学部, 講師 (10117939)
IIYORI Nobuyasu  Yamaguchi University, Education, Associate Professor, 教育学部, 助教授 (00241779)
木内 功  山口大学, 理学部, 助教授 (30271076)
片山 寿男  山口大学, 理学部, 教授 (00043860)
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2001: ¥1,800,000 (Direct Cost: ¥1,800,000)
KeywordsOF-ring / Nakayama ring / Harada ring / Skew-Matrix ring / extending module / lifting module / generalized relative injectivity / generalized relative projectivity / Artinian ring / Quasi-Frobenius ring / sjkew-matrix ring / Nakayama-permutation / Nakayama -automorphism / Artin環 / QF-環 / Nakayama環 / CS-加群 / Harada環 / Nakayama置換 / Nakayama自己同型
Research Abstract

(1) head investigator Oshiro has been extensively studied on Quasi-Frobeniu ring and Nakayama ring as applications of Harada rings (which was introduced by Oshiro). In research [1], Oshiro gave a survey on Harada ring and applications, most of which is due to Oshiro
(2) In [2],[3], we studied the open problem when direct sum of extending modules are extending modules. We readied to a situation that this problem should be studied by considering two types. In this paper, we completely solved on one type, by introducing generalized relative injectivity. Recently, this generalized relative injectivity is called "objectivity" (Oshiro injectivity)
(3)Dr Kuratomi is a student of the headinvestigator. In [6], he studied dual result of [3] and gave a very nice result.
(4) Oshiro [1],[2],[3], Baba [4], Koike [5], Kuratomi [6] are important papers for this research project. In particular, in [5], Koike discovered an exsample of a Quasi-Frobenius ring without Nakayama automorphism. This result is a very important and , in some sense, this paper completes the headinvestigator's many years study on Artinian rings.

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] [1]大城紀代市: "Theories of Harada in Artinian Rings and applications to classical Artinian Rings"International Symposium on Ring Theory. 279-301 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] [2]大城紀代市 他2人: "CS-property of direct sums of uniform modules"International Symposium on Ring Theory. 149-159 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] [3]大城紀代市 他2人: "On direct sums of extending modules and international exchange property"Journal of Algebra. 250. 115-133 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] [4]馬場良始: "On self-duality of Auslander rings of local serial rings"Communication in Algebra. 30. 2583-2592 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] [5]小池寿俊: "Examples of QF-rings without self-duality and H-rings without Nakayama automorphisms"Journal of Algebra. 241. 731-744 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] [6]倉富要輔: "On direct sum of lifting modules and international exchange property"Proc 35^<th> Symposium on Ring Theory. 35. 165-169 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kiyoichi Oshiro: "Theories of Harada in Artinian Rings and applications to classical Artinian Rings"International Symposium on Ring Theory, Trends in Math. 279-301 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kiyoichi Oshiro (with Yousuke Kuratomi etc.): "CS-property of direct sums of uniform modules"International Symposium on Ring Theory, Trends in Math. 149-159 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kiyoichi Oshiro (with Yousuke Kuratomi etc.): "On direct sums of extending modules and international exchange property"Journal of Algebra. 250. 115-133 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Yoshiaki Baba: "On self-duality of Auslander rings of local serial rings"Communication in Algebra. 30(6). 2583-2592 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kazutoshi Koike: "Examples of QF-rings without self-duality and H-rings without Nakayama automorphisms"Journal of Algebra. 241. 731-744 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Yousuke Kuratomi: "On direct sum of lifting modules and international exchange property"Proc 35^<th> Symposium on Ring Theory. 165-169 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 大城紀代市, 他2人: "On direct sums of Extending modules and Internal exchange property"Journal of Algebra. 250. 115-133 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 大城紀代市: "Theories of Harada in Artinian rings and application"Trend Math.. 149-159 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] 大城紀代市他, 2人: "CS-property of direct sums of uniform modules"Trend Math. 149-159 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] 久田見 守: "Regular rings with comparability and some related properties"Communication in Algebra. 30. 3337-3349 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 菊政 勲 他1人: "Commutative algebra radical cube zero"Communication in Algebra. 31. 1-12 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] 吉村 浩 他1人: "Some type of commutative artin algebra"数理解析研究所講究碌. 1222. 24-33 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 大城紀代市: "Theories of Harada in Artinian ring and application"Trends Math.. 279-301 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 大城紀代市 他2人: "On clinect sum of CS-modules and internal exchange property"Trends Math.. 149-159 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 大城紀代市 他2人: Journal of Algebra. (in appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] 久田見 守 他1人: "Unit regular rings satisfying weak comparability"Comminications in Argebra. 29(3). 1131-1140 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 木内 功: "On arithmetical functions related to Ramanu jan sum"Publ. Math. Rebrecen. 58(1〜2). 109-119 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 吉村 浩: "Some type of commutatine artin algebra"数理解析研究所講究録. 1222. 24-33 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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