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2011 Fiscal Year Final Research Report

A study of integrated orders and its applications

Research Project

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Project/Area Number 21540056
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokushima Bunri University

Principal Investigator

MARUBAYASHI Hidetoshi  徳島文理大学 (00034702)

Co-Investigator(Kenkyū-buntansha) 植田 玲  島根大学 (70213345)
Project Period (FY) 2009 – 2011
Keywords環論
Research Abstract

We have mainly studied the algebraic structure of the following five different types of rings.
(1) Let R be a partial skew polynomial ring over a semi-simple Artinain ring. We proved there are three different central idempotent in R. Furthermore we determined the structure of prime radical of R and proved that any prime ideals of R is either a maximal ideal and principal or idempotent.
(2) Let R be an Ore extension over a non-commutative valuation ring. We proved that R is always a generalized Bezout. Further we obtained that a necessary and sufficient conditions for R to be fully bounded.
(3) We classified the prime ideals of crossed product algebras over non-commutative valuation rings.
(4) We classified the localizing system of Prufer rings.
(5) We classified the prime ideals in skew polynomial rings over commutative Dedekind domain and determined the structure of the prime factor rings.

  • Research Products

    (7 results)

All 2012 2010 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (1 results) Book (1 results)

  • [Journal Article] Ore extensions over total valuation rings2010

    • Author(s)
      H. Marubayashi
    • Journal Title

      Algebras and Representation Theory

      Volume: 13

    • Peer Reviewed
  • [Journal Article] Partial skew polynomial rings over semisimple Artinian rings2010

    • Author(s)
      W. Cortes, M. Ferrero, H. Marubayashi and Y. Hirano
    • Journal Title

      Comm. in Algebras

      Volume: 38 Pages: 1663-1676

    • Peer Reviewed
  • [Journal Article] The group of divisors of an Ore extension over a Noetherian integrally closed domain2010

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

      The Aligarh Bulletin of Math

      Volume: 29(2) Pages: 1-4

    • Peer Reviewed
  • [Journal Article] Prime ideals in graded extensions for crossed product algebras

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

      Comm. in algebras

    • Peer Reviewed
  • [Journal Article] Prime factor rings of skew polynomial rings over a commutative Dedekind domain, to appear in Rockey Mountain

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

      J. of Math

    • Peer Reviewed
  • [Presentation] Prime factor rings of Ore extensions over a commutative Dedekind domain

    • Author(s)
      H. Marubayashi
    • Organizer
      International Conference on Algebra and its Applications(ICAA-10)
    • Place of Presentation
      Aligarh Muslim University, India
  • [Book] Prime Divisors and Non-commutative Valuation Rings2012

    • Author(s)
      H. Marubayashi and F. Van Oystaeyen
    • Total Pages
      218
    • Publisher
      Springer

URL: 

Published: 2013-07-31  

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