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On Artinian rings

Research Project

Project/Area Number 15540027
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionOsaka Kyoiku University

Principal Investigator

BABA Yoshitomo  Osaka Kyoiku University, Faculty of Education, Associate Professor, 教育学部, 助教授 (10201724)

Co-Investigator(Kenkyū-buntansha) KITAMURA Kazuo  Osaka Kyoku University, Department of Education, Professor, 教育学部, 教授 (30030381)
UNO Katsuhiro  Osaka Kyoku University, Department of Education, Professor, 教育学部, 教授 (70176717)
OSHIRO Kiyoichi  Yamaguchi University, Graduate school of Science and Engineering, Professor, 理学部, 教授 (90034727)
YOSHIMURA Hiroshi  Yamaguchi University, Graduate school of Science and Engineering, Associate Professor, 理学部, 助教授 (00182824)
Project Period (FY) 2003 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2005: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2004: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Keywordsring / R-module / Morita Self-duality / Harada ring / Nakayama ring
Research Abstract

In the theory of artinian rings, quasi-Frobenius rings ( QF-rings) and Nakayama rings (generalized uniserial rings) are important classical artinian rings. And, in the early 1980s, Manabu Harada found a new class of artinian rings which contain QF-rings and Nakayama rings. Now these new artinian rings are called Harada rings and the study of QF-rings and Nakayama ring from the point of view of Harada rings is very important.
It is well known that QF-rings and Nakayama rings have the Morita self-dualities. But recently it was showed that Harada rings do not have the Morita self-dialities in general. Our first aim is to give answers the question: What kind of Harada rings have the Morita self-dualities. To be specific, we study Harada rings of a component type. The class of Harada rings of a component type contains the class of Nakayama rings, and Nakayama rings are well characterized as a special kind of Harada rings of a component type. In addition, Harada rings of a component type have the Morita weakly symmetric self-dualities.
In [Y. Baba and K. Oshiro: On a theorem of Fuller, Journal of Algebra 154 (1994), 86-94], we study the famous Fuller's theorem which characterizes projective injective modules over artinian rings. This reseach is further studied by T. Sumioka, M. Hoshino, and M. Morimoto. On the other hand, in [Y. Baba: Injectivity of quasi-projective modules, projectivit.y of quasi-injective modules, and projective cover of injective modules, Journal of Algebra 155 (1994), 415--434], we characterized quasi-injective projective modules and quasi-projective injective modules. From this point of view, we studied the above Fuller's Theorem again.
"In addition to these studies, we write a lecture note titled ""Classical artinian rings and related topics"" which includes the above results and further umpublished results. This book will be published in several years"

Report

(5 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (23 results)

All 2006 2005 2004 2003 Other

All Journal Article (20 results) Publications (3 results)

  • [Journal Article] On quasi-projective modules and quasi-injective modules2006

    • Author(s)
      Yoshitomo Baba
    • Journal Title

      Scientiae Mathematicae Japonicas 63・1

      Pages: 589-596

    • NAID

      10020293227

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On quasi-projective modules and quasi-injective modules2006

    • Author(s)
      Yoshitomo Baba
    • Journal Title

      Scientiae Mathematicae Japonicae 63, 1

      Pages: 589-596

    • NAID

      10020293227

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Algebraic structure of association scheme of prime order2006

    • Author(s)
      Akihide Hanaki, Katsuhiro Uno
    • Journal Title

      Journal of Algebraic Combinatorics 23・2

      Pages: 189-195

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Elementary divisors of Cartan matrices for symmetric groups2006

    • Author(s)
      Katsuhiro Uno, Hiro-Fumi Yamada
    • Journal Title

      J. Math. Soc. Japan 58・4

      Pages: 1031-1036

    • NAID

      10018380794

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On quasi-projective modules and quasi-injective modules2006

    • Author(s)
      Yoshitomo Baba
    • Journal Title

      Scientiae Mathematicae Japonicae 63・1

      Pages: 589-596

    • NAID

      10020293227

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On Harada rings of a component type2005

    • Author(s)
      Yoshitomo Baba
    • Journal Title

      Advances in ring theory, World Sci. Publ., Mackensack, NJ

      Pages: 1-11

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On Harada rings of a component type2005

    • Author(s)
      Yoshitomo Baba
    • Journal Title

      Advances in ring theory (World Sci. Publ., Hackensack, NJ)

      Pages: 1-11

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Isomorphism classes of algebras with radical cube zero2005

    • Author(s)
      Isao Kikumasa, Hiroshi Yoshimura
    • Journal Title

      Advances in ring theory, World Sci.Publ.

      Pages: 106-117

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On Harada rings of a component type2005

    • Author(s)
      Yoshitomo Baba
    • Journal Title

      Advances in ring theory, World Sci.Publ.

      Pages: 1-11

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Direct sums of relative (quasi-) cuntinuous modules2004

    • Author(s)
      Chaehoon Chang, Kiyoichi Oshiro
    • Journal Title

      East-West J. Math. 6・2

      Pages: 125-130

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Conjectures on character degrees for the simple Thompson group2004

    • Author(s)
      Katsuhiro UNO
    • Journal Title

      Osaka J.Math. 41・1

      Pages: 11-36

    • NAID

      120004841877

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 行列を使った森田自己双対性の証明について2003

    • Author(s)
      岩瀬謙一, 馬場良始
    • Journal Title

      数学教育研究 33

      Pages: 139-148

    • NAID

      40006364270

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2004 Annual Research Report
  • [Journal Article] On Harada rings and quasi-Harada rings2003

    • Author(s)
      Yoshitomo Baba
    • Journal Title

      代数学シンポジゥム報告集 46

      Pages: 166-177

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Ken-ichi Iwase, On a proof of Morita self-duality using matrixs (Japanese)2003

    • Author(s)
      Yoshitomo Baba
    • Journal Title

      Reseach of Mathematical Education 33

      Pages: 139-148

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On Harada rings and quasi-Harada rings2003

    • Author(s)
      Yoshitomo Baba
    • Journal Title

      Proceeding of 48th Symposium of Algebra 48

      Pages: 166-177

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Self-duality of llarad a ring of a component type

    • Author(s)
      Yoshitomo Baba
    • Journal Title

      Journal of Algebra and Its Applications (Accepted)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Self-duality of Harada ring of a component type

    • Author(s)
      Yoshitomo Baba
    • Journal Title

      Journal of Algebra and Its Applications (Accepted)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Self-duality of Harada ring of a component type

    • Author(s)
      Yoshitomo Baba
    • Journal Title

      Journal of Algebra and Its Applications (Accepted)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Algebraic structure of association schemes of prime order

    • Author(s)
      Katsuhiro Uno, Akihide Hanaki
    • Journal Title

      Journal of Algebraic Combinatorics To appear

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Direct sums of relative (quasi-) continuous modules

    • Author(s)
      Kiyoichi OSHIRO
    • Journal Title

      East-West Journal of Math. (印刷中)

    • Related Report
      2004 Annual Research Report
  • [Publications] Yoshitomo BABA: "On Harada rings and quasi-Harada ring"代数学シンポジウム報告集. 48. 166-177 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Sawabe MASATO, Katsuhiro UNO: "Conjectures on character degrees for the simple Lyons group"Quart.J.Math.Oxford Ser.. 54・1. 103-121 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kikumasa ISAO, Hiroshi YOSHIMURA: "Commutative algebra with radical cube zero"Communications in Algebra. 31・4. 1837-1858 (2003)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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