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COMBINATORIAL SEMIGROUP THEORY AND ITS APPLICATIONS

Research Project

Project/Area Number 09640038
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionSHIMANE UNIVERSITY

Principal Investigator

UEDA Akira  SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING ASSOCIATED PROFESSOR, 総合理工学部, 助教授 (70213345)

Co-Investigator(Kenkyū-buntansha) KAMIYA Noriaki  SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING ASSOCIATED PROFESSOR, 総合理工学部, 助教授 (90144691)
KIKKAWA Michihiko  SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING PROFESSOR, 総合理工学部, 教授 (70032430)
MIWA Takuo  SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING PROFESSOR, 総合理工学部, 教授 (60032455)
ENDO Michiro  SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING ASSOCIATED PROFESSOR, 総合理工学部, 助教授 (40211916)
IMAOKA Teruo  SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING PROFESSOR, 総合理工学部, 教授 (60032603)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1998: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1997: ¥1,900,000 (Direct Cost: ¥1,900,000)
Keywordscombinatorial semigroup theory / automaton / algorithm / amalgamation base / valuation ring / universal algebra / loop / representation / 組合せ半群 / 一般代数系 / 融合 / 正則半群 / ホップ代数 / 非可換付値環
Research Abstract

1. Decision problem whether or not a finite semigroup has a certain property (P) has been studied by many mathematicians, and Spair and Guba proved that for many properties (P) the decision problem is undecidable. Concerning this problem, Shoji proved that there exists an algorithm to decide whether or not a finite semigroup has the representation extension property. Furthermore, shoji proved the following results
(1) For completely 0-simple semigroup S, the following are equivalent.
(i) S is a special amalgamation base.
(ii) S is either left absolutely flat or right absolutely flat.
(iii) S satisfies either left annihilator condition or right annihilator condition.
(2) For finite commutative semigroup T, the following are equivalent.
(i) T is a completely special amalgamation base.
(ii) T is completely amalgamation base.
(iii) T is E-separable.
2. As applications of combinatorial semigroup theory we obtained the following results.
(1) Imaoka investigated about representations of generalized inverse *-semigroups.
(2) Ueda studied about Prufer orders in simple Artinian rings. In particular, Ueda characterized branched and unbranched prime ideals of Prufer orders.
(3) Kondo gave an axiom system of a non-linear 4-valued logic , whose Lindenbaum algebra is the de Morgan algebra with implication.
(4) Miwa obtained a new characterization of superparacompact spaces. Miwa also defined new covering properties and studied invariance and inverse invariance under various maps of these covering properties.
(5) Kikkawa introduced the algebraic concept of projectivity of a Lie triple algebra and investigated about properties of Lie algebra of projectivity.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report

Research Products

(30 results)

All Other

All Publications (30 results)

  • [Publications] Peter Higgins: "On special amalgamation bases" Proceedings of the conference on Semigroup and Applications. 87-96 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.E.Hall: "Representations and Amalgamation of Generalized Inverse* Semigroups" Semigroup Forum. 58. 126-141 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hidetoshi Marubayashi: "Idealizers of Semi-hereditary v-orders" Mathematica Japonica. 45. 51-56 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Michiro Kondo: "Characterization theorem of 4-valued de Morgan logic" Memoirs of the faculty of science and engineering Shimane University. 31. 73-80 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Michiro Kondo: "A note on the regular projections in equivalential algebras" Far East Journal of Mathematical Science. 1・2. 167-174 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] D.Buhagiar: "On superparacompact and Lindelof Go-spaces" Houston Journal of Mathematics. 24・3. 443-457 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Imaoka: "Proceedings of the Workshop on Language, Computation and Algebra" Kobe University, 89 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hidetoshi Marubayashi: "Non-commutative Valuation Rings and Semi-Hereditary Orders" Kluwer Academic Publisher, 191 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Peter Higgins: "On special amalgamation bases" Proceedings of the conference on Semigroup and Applications, World Scientific. 87-96 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.E.Hall: "Representations and Amalgamation of Generalized Inverse ^*-Semigroups" Semigroup, Forum. Vol.58. 126-141 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hidetoshi Marubayashi: "Idealizers of Semi-hereditary-v-orders" Mathematica Japonica. Vol.45. 51-56 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Michiro Kondo: "Characterization theorem of 4-valued de Morgan logic" Memoirs of the faculty of science and engineering Shimane University, Ser.B. Vol.31. 73-80 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Michiro Kondo: "A note on the regular projections in equivalential algebras" Far East Journal of Mathematical Science. Vol.1 (2). 167-174 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] D.Buhagiar and T.Miwa: "On superparacompact and Lindelof GO-spaces" Houston Journal of Mathematics. Vol.24, No.3. 443-457 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Imaoka: Proceedings of the Workshop on Language, Computation and Algebra, Kobe University. 89 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hidetoshi Marubayashi, Haruo Miyamaoto and Akira Ueda: "Non-commutative Valuation Rings and Semi-Heraditary Orders" Kluwer Academic Publishers. 191 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] P.Higgins: "On special amalgamation bases" Proceedings of the conference on Semigroupand Applications. 87-96 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.E.Hall: "Representations and Amalgamation of Generalized Inverse *-semigroups" Semigroup Forum. 58. 126-141 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Michiro Kondo: "Characterization Thoorem of 4-valued de Morgan Logic" Memoirs of the faculty of science and Engineering Shimane University. 31. 73-80 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Michiro Kondo: "Note on the BCI-G part of BCI-algebras" Mathematica Japonica. 48・3. 349-352 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Michiro Kondo: "A Note on the regular projections in equivalential algebras" Far East Journal of Mathematical Science. 1・2. 167-174 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] D.Buhagiar: "On superpara compact and Lindelof GO-spaces" Houston Journal of Mathematics. 24・3. 443-457 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Imaoka: "Some remarks on representations of generalized inverse *-semigroups" Memoirs of the faculty of science and engineering Shimane Univ.B,30. 23-35 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Kondo: "Functional Freeness for thce Berman Class Km,u of Ockham algebras" Hemoirs of the faculty of science and engineering Shimane Univ.B.30. 49-55 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Imaoka: "Repvesentations and amalgamation of generalozed inverse *-semigroups" Semigroup Forum. 55. 247-255 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] A.Masuoka: "Calculations of some groups of Hopf algebra extensions" Journal of Algebra. 191,2. 568-588 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] A.Masuoka: "Faithfully flat forms and cohomology of Hopf algebra extensions" Commuu : cation in Algebra. 25,4. 1169-1197 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Marubayashi: "Idealizers of semi-hereditary v-orders" Mathematica Japonica. 45,1. 51-56 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Imaoka: "Proceedings of the Workshop on Languages,Computation and Algebra" Kobe University, 89 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Marubayashi: "Non-commutative valuation rings and semi-hereditary orders" Kluwer Academic Publishers, 191 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-03-31   Modified: 2016-04-21  

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