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Combinatorial semigroup theory and its applications

Research Project

Project/Area Number 13640023
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

SHOJI Kunitaka  Shimane University, Mathematics, Professor, 総合理工学部, 教授 (50093646)

Co-Investigator(Kenkyū-buntansha) FUJITA Kenetsu  Shimane University, Information, Assistant Professor, 総合理工学部, 助教授 (30228994)
MIWA Takuo  Shimane University, Mathematics, Professor, 総合理工学部, 教授 (60032455)
IMAOKA Teruo  Shimane University, Mathematics, Professor, 総合理工学部, 教授 (60032603)
OZAKI Manabu  Shimane University, Mathematics, Assistant Professor, 総合理工学部, 助教授 (80287961)
UEDA Akia  Shimane University, Mathematics, Assistant Professor, 総合理工学部, 助教授 (70213345)
近藤 通朗  島根大学, 総合理工学部, 助教授 (40211916)
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: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2001: ¥2,000,000 (Direct Cost: ¥2,000,000)
Keywordssemigroup / amalgam / algorithm / fibre / homotopy / rewriting system / caluculus / Iwasawa theory / レトラクト / 岩沢不変 / 群 / 融合問題 / 語の問題 / 自由融合積 / メンバーズシップ問題 / 不値環
Research Abstract

(1) There is no solution of the problem whether or not there exists an algorithm to decide if a finite semigroup is an amalgamation base for all semigroups. On the other hand, it is known that a semigroup which is an amalgamation base for all semigroups always has the representation extension property. In this project, we prove that there exists an algorithm to decide if a finite semigroup has the representation extension property. Also, it is known that a completely 0-simplesemigroup with the representation extension property is an amalgamation base for all semigroups. However, we can construct by the software "Mathematic" an example of a finite regular semigroup with the representation extension property and without being an amalgamation base for all semigroups. Moreover, we prove that there exists an algorithm to decide if a finite semigroup is left absolutely flat. The result will appear in a forthcoming paper. (2) We prove that a finite semigroup which is an amalgamation for all finite semigroups has the representation extension property. As a consequence, we decide the structure of finite bands which is an amalgamation for all finite semigroups. (3) We give another proof of Okininski and Putcha's theorem on finite inverse semigroup, which is a natural extension of B.Neumann's result on group. (4) We show that the construction of λ μ-models can be given by the use of a fixed point operator and the Godel-Gentzen translation. (5) We study the fibrewise homotopy, fibrewise fibration and fibrewise cofibration. (6) Let p be an odd prime number. By using Iwasawa theory we construct cyclotopic fields whose maximal real subfields have class group with arbitrarily large p-rank and a conductor with only four prime factors.

Report

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

Research Products

(25 results)

All Other

All Publications (25 results)

  • [Publications] K.Shoji: "Regular semigroups which have (REP) and (REP)^<op> is not necessarily amalgamation bases"Semigroup Forum. 63. 223-236 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Shoji: "Commutative semigroups which are semigroup amalgamation bases"Journal of Algebra. 238. 1-50 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.E.Hall, K.Shoji: "Finite bands and amalgamation bases for finite semigroups"Communications in algebra. 30. 911-933 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Fujita: "An Interpretation of λμ-calculucs in λ-calculucs"Information Processing Letters. 84. 261-264 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Hotta, T.Miwa: "A new approach to fibrewise fibration and cofibrations"Topology and its application. 122. 205-222 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Ozaki: "An application of Iwasawa theory to constructing fields Q(ζ+ζ^<-1>) which have class group with large p-rank"Nagoya Journal of Mathematics. (To appear). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K,Shoji.: "Regular semigroups which have (REP) and (REP)^<op> is not necessarily amalgamation bases"Semigroup Forum. 63. 223-236 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K,Shoji.: "Commutative semigroups which are semigroup amalgamation bases"J. Algebra. 238. 1-50 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K,Shoji.: "Finite bands and amalgamation bases for finite semigroups"Communication in algebras, (with T.E. Hall). 30. 911-933 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K,Fujita.: "An Interpretation of λμ-calculucs in λ-calculucs"Inform. Process. Lett.. 84. 261-264 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T,Miwa.: "A new approach to fibrewise fibration and cofibrations"Topology and its applications, (with Y.Hotta). 122. 205-222 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M,Ozaki.: "An application of Iwasawa theory to constructing fields Q (ζ+ζ^<-1>) which have class group with large p-rank"Nagoya J. Math., To appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Shoji: "Commutative semigroups which are amalgamation bases"Journal of Algebra. 238. 1-50 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.E.Hall: "Finite bands and amalgamation bases for finite semigroups"Communications in Algebra. 30. 911-933 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Imaoka: "Characterization of locally^*-inverse semigroups"Scientiae Math. Japonica. 7. 47-53 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Hotta: "A new approach to fibrewise fibrations and cofibrations"Topology and its applications. 122. 205-222 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Fujita: "An interpretation of λμ-calucus in λ-calucus"Information processing letters. 84. 261-264 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Ozaki: "Iwasawa λ_{3}-invariants of certain cubic fields"Acta Arithmetica. 97. 387-398 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Shoji: "A proof of Okninski and Putcha's theorem"Proc.of the Third Inter. Colloq.on Words, languages and Combinatorics, Ed. by M. Ito, \ & T. Imaoka, World Scientific. (To appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Imaoka: "Prehomomorphisms on locally inverse ^<*->semigroups"Words, Semigroups, and Transductions, edited by M. Ito, G. Paun and S. Yu, World Scientific, Singapore. 203-209 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Imaoka: "Some remarks on generalized inverse ^<*->semigroups"Algebraic Semigroups, Formal Languages and Computation RIMS Kokyuroku. No.1222. 1-4 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Hotta: "A new approach to fibrewise fibrations and cofibrations"Top.Appl.. (To appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Kondo: "Relationship between ideals of BCI-algebras and order ideals of its adjoint semigroup"International Jour.of Math. and Math. Sci.. (To appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] H.H.Burngs: "A classification of primary ideals of Dubrovin valuation rings"Houston Journal of Mathematics. (To appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Imaoka: "Proceedings of the 5th Symposium on Algebra, Languages and Computation, Shimane Univ."Shimane University. 86 (2002)

    • Related Report
      2001 Annual Research Report

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Published: 2001-03-31   Modified: 2016-04-21  

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