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A unified theory of Grobner bases and an application to syzygies of modules

Research Project

Project/Area Number 21540048
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KOBAYASHI Yuji  東邦大学, 理学部, 訪問教授 (70035343)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2011: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywordsグレブナー基底 / シチジー / 書き換えシステム / 順序半群 / イデアル / 加群 / 完備化 / 書換えシステム / モジュラー計算 / 複雑度 / チューリング機械 / 危険対 / シチジー加群 / アルゴリズム / ホモロジー有限性 / コホモロジー
Research Abstract

We develop a unified theory of Grobner bases, and apply it to various calculations concerning algebras, ideals and modules. We construct a theory on an algebra F based on a well-ordered semigroup and on a projective F-module FX, and we prove the critical pair theorem. We obtain a main result that the cycles made from critical pairs in FH form a generating system of syzygies, if H is a Grobner basis on FX.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (22 results)

All 2012 2011 2010 2009

All Journal Article (13 results) (of which Peer Reviewed: 10 results) Presentation (7 results) Book (2 results)

  • [Journal Article] The complexity of string rewriting systems2012

    • Author(s)
      Yuji Kobayashi
    • Journal Title

      Theoretical Computer Science

      Volume: Vol.438 Pages: 1-12

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The derivational complexity of string rewriting systems2012

    • Author(s)
      Yuji Kobayashi
    • Journal Title

      Theoretical Computer Science

      Volume: (未定)(印刷中)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A short history of repetition-free words2011

    • Author(s)
      Yuji Kobayashi
    • Journal Title

      RIMS Kokyuroku

      Volume: 1769 Pages: 101-110

    • Related Report
      2011 Annual Research Report
  • [Journal Article] Grobner bases and syzygies on modules over algebras based on well-ordered semigroups2010

    • Author(s)
      Yuji Kobayashi
    • Journal Title

      International Journal of Pure and Applied Mathematics

      Volume: Vol.64 Pages: 457-489

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Grobner on algebras based on well-ordered semigroups, Automata2010

    • Author(s)
      Yuji Kobayashi
    • Journal Title

      Formal Languages and Algebraic Systems, World Scientific

      Volume: Vol.64 Pages: 85-102

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The homological finiteness properties left-, right-and bi-FP_n of monoids2010

    • Author(s)
      Yuji Kobayashi
    • Journal Title

      Communications in Algebra

      Volume: Vol.38 Pages: 1-12

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 3D Conway's solitaire2010

    • Author(s)
      Yuji Kobayashi, Kaname Nakazawa, Yohei Kobayashi
    • Journal Title

      Recreational Mathematics

      Volume: Vol.35 Pages: 193-201

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The homological finiteness properties left-, right- and bi-FP_n of monoids2010

    • Author(s)
      Yuji Kobayashi
    • Journal Title

      Communications in Algebra

      Volume: 38 Pages: 1-12

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Groebner bases on algebras based on well ordered Semigroups2010

    • Author(s)
      Yuji Kobayashi
    • Journal Title

      Automata, Formal Languages and Algebraic Systems

      Pages: 85-102

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Groebner bases and syzygies of algebras and modules based on well-ordered semigroups2010

    • Author(s)
      Yuji Kobayashi
    • Journal Title

      International Journal of Pure and Applied Mathematics

      Volume: 64 Pages: 457-489

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 3D Conway's solitaire2010

    • Author(s)
      Y Kobayashi, K Nakazawa
    • Journal Title

      Journal of Recreational Mathematics 35

      Pages: 193-201

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Grobner bases on projective bimodules and the Hochschild cohomology Part IV2009

    • Author(s)
      Yuji Kobayashi
    • Journal Title

      RIMS Kokyuroku

      Volume: vol.1655 Pages: 132-139

    • Related Report
      2011 Final Research Report
  • [Journal Article] Groebner bases on projective bimodules and the Hochschild cohomology Part IV2009

    • Author(s)
      Yuji Kobayashi
    • Journal Title

      RIMS Kokyuroku 1655

      Pages: 132-139

    • Related Report
      2009 Annual Research Report
  • [Presentation] Term orders and the modular algorithms for Grobner bases,代数系および計算機科学基礎2012

    • Author(s)
      Yuji Kobayashi
    • Place of Presentation
      京都大学
    • Year and Date
      2012-02-22
    • Related Report
      2011 Final Research Report
  • [Presentation] Term orders and the modular algorithms for Groebenr bases2012

    • Author(s)
      Yuji Kobayahsi
    • Organizer
      代数系および計算機科学基礎
    • Place of Presentation
      京都
    • Year and Date
      2012-02-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] A short history of repetition-free words, 代数と言語のアルゴリズムと計燦理論2011

    • Author(s)
      Yuji Kobayashi
    • Place of Presentation
      京都大学
    • Year and Date
      2011-02-23
    • Related Report
      2011 Final Research Report
  • [Presentation] A short history of repetition words2011

    • Author(s)
      Yuji Kobayashi
    • Organizer
      Algebra, Language and Computation
    • Place of Presentation
      京都大学数理科学研究所(京都府)
    • Year and Date
      2011-02-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] 代数・書換え・計算2010

    • Author(s)
      小林ゆう治
    • Organizer
      代数セミナー
    • Place of Presentation
      城西大学
    • Year and Date
      2010-12-20
    • Related Report
      2011 Final Research Report
  • [Presentation] The complexity of string-rewriting systems, 代数と言語のアルゴリズムと計燦理論2010

    • Author(s)
      Yuji Kobayashi
    • Place of Presentation
      京都大学
    • Year and Date
      2010-02-19
    • Related Report
      2011 Final Research Report
  • [Presentation] The derivational complexities of string rewriting systems2010

    • Author(s)
      小林ゆう治
    • Organizer
      研究集会「代数と言語のアルゴリズムと計算理論」
    • Place of Presentation
      京都大学
    • Year and Date
      2010-02-19
    • Related Report
      2009 Annual Research Report
  • [Book] Automata, Formal Languages and Algebraic Systems2010

    • Author(s)
      Masami Ito, Yuji Kobayashi, Kunitaka Shoji
    • Total Pages
      244
    • Publisher
      World Scientific
    • Related Report
      2011 Final Research Report
  • [Book] Automata, Formal Languages and Algebraic Systems2010

    • Author(s)
      M.Ito, Y.Kobayashi, T.Shoji(ed.)
    • Total Pages
      236
    • Publisher
      World Scientific
    • Related Report
      2010 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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