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The integrated study of orders and valuation rings

Research Project

Project/Area Number 24540058
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionTokushima Bunri University

Principal Investigator

Marubayashi Hidetoshi  徳島文理大学, 理工学部, 教授 (00034702)

Co-Investigator(Kenkyū-buntansha) Ueda Akira  島根大学, 総合理工学研究科(研究院), 教授 (70213345)
Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords環論 / イデアル / 極大整環 / 付値環 / 遺伝的環 / 整環 / Ideal / HNP ring / G-HNP ring / Skew polynomial ring / Differentail polynomial / Ore extension / Ore extension / 国際情報交換、トルコ / Asano整環 / Dedekind prime ring
Outline of Final Research Achievements

We study orders and valuation rings. About order theory, ① we give the necessary and sufficient conditions for the ring of Morita contexts to be maximal orders in terms of modules theory.② we obtain that the necessary and sufficient conditions for skew polynomial rings and differential polynomial rings to be generalized Asano rings. ③we completely describe the structure of projective ideals in skew polynomial rings over hereditary rings, which leads us to find a new class of rings being called "generalized hereditary rings".
About the study of valuation rings,④we study prime ideals in graded extensions for crossed product algebras.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (17 results)

All 2016 2015 2014 2013 2012

All Journal Article (11 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 11 results,  Open Access: 3 results,  Acknowledgement Compliant: 3 results) Presentation (5 results) (of which Int'l Joint Research: 1 results,  Invited: 3 results) Book (1 results)

  • [Journal Article] Ore-Rees rings which are maximal orders2016

    • Author(s)
      M.R.Helmi, H.Marubayashi, A.Ueda
    • Journal Title

      J. of Math Soc. Japan

      Volume: 68 Pages: 405-423

    • NAID

      130005122695

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Multiplicative ideal theory in non-commutative rings2016

    • Author(s)
      E.Akalan, H.Marubayashi
    • Journal Title

      Proceedings of Graz conference, Springer

      Volume: 1 Pages: 10-37

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Rings of Morita contexts which are maximal orders2015

    • Author(s)
      E.Akalan,P.Aydogdu, H.Marubayashi, B.Sarac
    • Journal Title

      J. Algebra and Its Applications

      Volume: 15 Pages: 1-13

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Ore-Rees rings which are maximal orders2015

    • Author(s)
      M.R.Helmi, H.Marubayashi and A.Ueda
    • Journal Title

      Journal of Math. Soc. Japan

      Volume: 67 Pages: 25-48

    • NAID

      130005122695

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Skew polynomial rings which are generalized Asano prime rings2013

    • Author(s)
      H.Marubayashi, I.Muchtadi-Alamasyah and A.Ueda
    • Journal Title

      J. of Algebra and Its Applications,

      Volume: 12(7) Pages: 15-23

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Differential polynomial rings which are generalized Asano prime rings2013

    • Author(s)
      M.R.Helmi, H. Marubayashi and A.Ueda
    • Journal Title

      Indian Pure and Appl. Math.

      Volume: 44(5) Pages: 1-9

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Bounded generalized Dedekind prime rings2013

    • Author(s)
      E.Akalan, M.R.Helmi, H.Marubayashi and A.Ueda
    • Journal Title

      Bull. Math. Soc. Sci. Math. Roumanie

      Volume: 56(1) Pages: 25-31

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Graded extensions in a skew Laurent polynomial ring2012

    • Author(s)
      H.Marubayashi and Y.Xie
    • Journal Title

      Southeast Asian Bulletin of Mathematics

      Volume: 36 Pages: 441-447

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Prime ideals in graded extensions for crossed products algebras2012

    • Author(s)
      H.Brungs, H.Marubayashi and E.Osmanagic
    • Journal Title

      Communications in Algebra

      Volume: 40 Pages: 1951-1973

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Skew Rees rings which are maximal orders2012

    • Author(s)
      M.R.Helmi, H.Marubayashi and A.Ueda
    • Journal Title

      Proceedings of the 45th Symposium on Ring Theory and Representation Theory

      Volume: 45 Pages: 39-45

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Prime factor rings of skew polynomial rings over a commutative Dedekind domain2012

    • Author(s)
      A.K.Amir,H.Marubayashi and W.Wang
    • Journal Title

      Rockey Mountain Journal of Mathemtaics

      Volume: 42 Pages: 2055-2073

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Generalized hereditary Noetherian prime rings2016

    • Author(s)
      H.Marubayashi
    • Organizer
      International Coference on Algebra and its Applications
    • Place of Presentation
      Aligarh Muslim Univ. India
    • Year and Date
      2016-11-12
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Examples of Ore extensions which are maximal orders whose based rings are not maximal orders2015

    • Author(s)
      H.Marubayashi, A.Ueda
    • Organizer
      Proceedings of the 48th Symposium on Rings Theory and Representation Theory
    • Place of Presentation
      Nagoya UNiv.
    • Year and Date
      2015-10-01
    • Related Report
      2015 Annual Research Report
  • [Presentation] Ore and Ore-Rees rings which are maximal orders2014

    • Author(s)
      H.Marubayashi
    • Organizer
      Arithmetic and Ideal Theory of Rings and Semigroups
    • Place of Presentation
      University of Graz, Austria
    • Year and Date
      2014-09-22 – 2014-09-26
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Differential Rees rings which are maximal orders2014

    • Author(s)
      H. Marubayashi
    • Organizer
      International Conference on Recent Trends in Algebra and Analysis with Applications, Aligarh Muslim Univ. India
    • Place of Presentation
      Aligarh Muslim University, India
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Skew Rees rings which are maximal orders2012

    • Author(s)
      M.R.Helmi, H.Marubayashi and A.Ueda
    • Organizer
      45th Symposium of Ring Theory and Representation Theory
    • Place of Presentation
      Shinnshu University
    • Related Report
      2012 Research-status Report
  • [Book] Prime Divisors and Noncommutative Valuation Theory2012

    • Author(s)
      H.Marubayashi and F.Van Oystaeyen
    • Total Pages
      218
    • Publisher
      Springer
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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