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2007 Fiscal Year Final Research Report Summary

Representations of regular*-semigroups and their application to partial symmetry

Research Project

Project/Area Number 17540025
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

IMAOKA Teruo  Shimane University, Interdisciplinary faculty of Science and Engineering, Professor (60032603)

Co-Investigator(Kenkyū-buntansha) SHOJI Kunitaka  Shimane University, Interdisciplinary faculty of Science and Engineering, Professor (50093646)
KIMURA Makoto  Shimane University, Interdisciplinary faculty of Science and Engineering, Professor (30186332)
HATTORI Yasunao  Shimane University, Interdisziplinary faculty of Science and Engineering, Professor (20144553)
Project Period (FY) 2005 – 2007
Keywordsalgebra / *-semigroup / regular semigroup / renresentation / argorithm / geometry / topology / partial symmetry
Research Abstract

The purpose of this research is to study the representations of regular *-semigroups and their application to partial symmetry. During the term of our project, the head investigator obtained the following. For the results of other investigators and their detail, see the references in the larar.
1. By introducing the concept "biarrowed word tree", we obtained that the free generalized inverse *-semigroup is isomorphic to the set of all biarrowed word tree in respect to the new product.
2. The category of locally inverse *-semigroups and prehomomorphisms [homomorphisms] is isomorphic to the category of locally inductive *-groupoids and ordered functors [inductive functors].
3. By introducing the concept "PG^*-quintet", we constructed a PG^semigroup. And we showed that a generalized inverse *-semigroup S is E-unitary if and only if S is isomorphic to a PG^*-semigroup.
4. Any generalized inverse *-semigroup can be embedded in a *-complete, infinitely distributive generalized inverse *-semigroup.
5. We characterized a congruence on a generalized inverse *-semigroup by using the concept "*-congruence pair"

  • Research Products

    (63 results)

All 2008 2007 2006 2005 Other

All Journal Article (30 results) (of which Peer Reviewed: 9 results) Presentation (31 results) Book (2 results)

  • [Journal Article] Lagrangian submanifolds with codimension 1 totally geodesic foliatio-in complex projective spaces2008

    • Author(s)
      M. Kimura
    • Journal Title

      Kodai Math. J. 31

      Pages: 38-45

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Lagrangian submanifolds with codimension 1 totally geodesic foliation in complex projective spaces2008

    • Author(s)
      M. Kimura
    • Journal Title

      Kodai Math. J 31

      Pages: 38-45

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Finitely generated semigroups with regular congruence classes2007

    • Author(s)
      K. Shoji
    • Journal Title

      RIMS Kokyuroku 1562

      Pages: 127-131

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Fundamental theorems of lagrangian surfaces in S^2×S^22007

    • Author(s)
      M. Kimura and K. Suizu
    • Journal Title

      Osaka J. Math. 44

      Pages: 829-850

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Pseudo-holomorphic sectional curvatures of real hypersurfaces in a complex space form2007

    • Author(s)
      J. T. Cho and M. Kimura
    • Journal Title

      Kyushu J. Math. 62

      Pages: 1-13

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] There is no upper bound of small transfinite compactness degree in metrizable spaces2007

    • Author(s)
      V. A. Chatyrko and Y. Hattori
    • Journal Title

      Topology Appl. 154

      Pages: 1314-1320

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Fundamental theorems of lagrangian surfaces in S^2×S^22007

    • Author(s)
      M. Kimura, K. Suizu
    • Journal Title

      Osaka J. Math 44

      Pages: 829-850

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Pseudo-holomorphic sectional curvatures of real hypersurfaces in a complex space form2007

    • Author(s)
      J. T. Cho, M. Kimura
    • Journal Title

      Kyushu J. Math 62

      Pages: 1-13

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] There is no upper bound of small transfinite compactness degree in metrizable spaces2007

    • Author(s)
      V. A. Chatyrko, Y. Hattori
    • Journal Title

      Topology Appl 154

      Pages: 1314-1320

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] computation and their applications2007

    • Author(s)
      K. Shoji, Algebra, languages
    • Journal Title

      RIMS, Kyoto Univ

      Pages: 154

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Some remarks on generalized inverse *-semigroups2006

    • Author(s)
      T. Imaoka and T. Iigai
    • Journal Title

      RIMS Kokyuroku 1503

      Pages: 17-23

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Finite semigroups and decidability of amalgamation bases for semigroups2006

    • Author(s)
      K. Shoji
    • Journal Title

      RIMS Kokyuroku 1503

      Pages: 24-29

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Partitions of spaces by locally compact subspaces2006

    • Author(s)
      V. A. Chatyrko, Y. Hattori and H. Ohta
    • Journal Title

      Houston J. Math. 32

      Pages: 1077-1091

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Some remarks on generalized inverse *-semigroups2006

    • Author(s)
      T. Imaoka, T. Iigai
    • Journal Title

      RIMS Kokyuroku 1503

      Pages: 17-23

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Partitions by locally compact subspaces2006

    • Author(s)
      V. A. Chatyrko, Y. Hattori, H. Ohta
    • Journal Title

      Houston J. Math 32

      Pages: 1077-1091

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Algorithmic problems in algebra, languages and computation systems2006

    • Author(s)
      K. Shoji
    • Journal Title

      RIMS, Kyoto Univ

      Pages: 163

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Some remarks on ordered *-groupoids2005

    • Author(s)
      T. Imaoka and T. Isobe
    • Journal Title

      RIMS Kokyuroku 1437

      Pages: 116-118

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Syntactic monoids and languages2005

    • Author(s)
      T. Mitoma and K. Shoji
    • Journal Title

      RIMS Kokyuroku 1437

      Pages: 11-16

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Congruence classes of Frenet curves in complex quadrics2005

    • Author(s)
      M. Kimura and M. Ortega
    • Journal Title

      J. Geom. 83

      Pages: 121-136

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Real hypersurfaces some of whose geodesics are plane curves in nonflat complex space forms2005

    • Author(s)
      T. Adachi, M. Kimura and S. Maeda
    • Journal Title

      Tohoku Math. J. 57

      Pages: 223-230

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Some remarks on ordered *-groupoids2005

    • Author(s)
      T. Imaoka, T. Isobe
    • Journal Title

      RIMS Kokyuroku 1437

      Pages: 116-118

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Syntactic monoids and languages2005

    • Author(s)
      T. Mitoma, K. Shoji
    • Journal Title

      RIMS Kokyuroku 1437

      Pages: 11-16

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Congruence classes of Frenet curves in complex quadrics2005

    • Author(s)
      M. Kimura, M. Ortega
    • Journal Title

      J. Geom 83

      Pages: 121-136

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Real hypersurfaces some of whose geodesics are plane curves in nonflat complex space forms2005

    • Author(s)
      T. Adachi, M. Kimura, S. Maeda
    • Journal Title

      Tohoku Math. J 57

      Pages: 223-230

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Completions of generalized inverse *-semigroups

    • Author(s)
      H. Ohta and T. Imaoka
    • Journal Title

      RIMS Kokyuroku (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Addition and product theorems for ind

    • Author(s)
      V. A. Chatyrko and Y. Hattori
    • Journal Title

      Theoret. Comput. Sci. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Lawson topology of the space of formal balls and hyperbolic topology

    • Author(s)
      H. Tsuiki and Y. Hattori
    • Journal Title

      Topology Appl. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Completions of generalized inverse *-semigroups

    • Author(s)
      H. Ohta, T. Imaoka
    • Journal Title

      RIMS Kokyuroku to appear

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Addition and product theorems for ind

    • Author(s)
      V. A. Chatyrko, Y. Hattori
    • Journal Title

      Theoret. Comput. Sci (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Lawson topology of the space of formal balls and Hyperbolic topology

    • Author(s)
      H. Tsuiki, Y. Hattori
    • Journal Title

      Topology Appl (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Completions of generalized inverse *-semigroups2008

    • Author(s)
      H. Ohta and T. Imaoka
    • Organizer
      京都大学数理解析研究所研究集会「代数, 言語のアルゴリズムと計算理論」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      20080200
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Representations of generalized inverse *-semigroups2008

    • Author(s)
      H. Ohta and T. Imaoka
    • Organizer
      第11回「代数, 言語と計算」シンポジウム
    • Place of Presentation
      京都産業大学
    • Year and Date
      20080200
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Syntactic monoids of contex-free languages2008

    • Author(s)
      K. Shoji
    • Organizer
      京都大学数理解析研究所研究集会「代数, 言語のアルゴリズムと計算理論」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      20080200
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Completions of generalized inverse *-semigroups2008

    • Author(s)
      H. Ohta, T. Imaoka
    • Organizer
      Workshop on Algorithms and Computational theory in Algebra and Languages
    • Place of Presentation
      RIMS, Kyoto Univ
    • Year and Date
      20080200
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Representations of generalized inverse *-semigroups2008

    • Author(s)
      H. Ohta, T. Imaoka
    • Organizer
      The 11th Sympo. on Algebra, Languages and Computation
    • Place of Presentation
      Kyoto Sangyo Univ. Workshop on Algebra, Languages
    • Year and Date
      20080200
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Finitely generated semigroups with regular congruence classes2008

    • Author(s)
      K. Shoji
    • Organizer
      Computation and their Applications
    • Place of Presentation
      RIMS, Kyoto Univ
    • Year and Date
      20080200
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Syntactic monoids of contex-free languages2008

    • Author(s)
      K. Shoji
    • Organizer
      Workshop on Algorithms and Computational Theory in Algebra and Languages
    • Place of Presentation
      RIMS, Kyoto Univ
    • Year and Date
      20080200
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Cosets in classes of regular *-semigroups2008

    • Author(s)
      H. Ohta and T. Imaoka
    • Organizer
      平成19年度日本数学会中国・四国支部例会
    • Place of Presentation
      山口大学
    • Year and Date
      20080100
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Cosets in classes of regular *-semigroups2008

    • Author(s)
      H. Ohta, T. Imaoka
    • Organizer
      Annual Meeting of Chugoku-Sikoku Branch of Japan Math. Soc
    • Place of Presentation
      Yamaguchi Univ
    • Year and Date
      20080100
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] The hyperbolic topology of normed linear spaces2007

    • Author(s)
      Y. Hattori and H. Tsuiki
    • Organizer
      International Conference in Topology and its Applications 2007 at Kyoto, jointly with 4th Japan-Mexico Topology Conference
    • Place of Presentation
      京都大学
    • Year and Date
      20071200
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] The hyperbolic topology of normed linear spaces2007

    • Author(s)
      Y. Hattori, H. Tsuiki
    • Organizer
      Internat. Conf. on Topology and its Appl., jointly with 4th Japan-Mexico Topology Conf
    • Place of Presentation
      Kyoto Univ
    • Year and Date
      20071200
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Finitely generated semigroups with regular congruence classes2007

    • Author(s)
      K. Shoji
    • Organizer
      京都大学数理解析研究所研究集会「代数, 形式言語, 計算システム理論とその応用」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      20070200
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] 複素2次局面内の合同性2006

    • Author(s)
      M. Kimura
    • Organizer
      第53回幾何学シンポジウム
    • Place of Presentation
      金沢大学
    • Year and Date
      20060800
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Around sum theorems for small inductive dimension2006

    • Author(s)
      V. Chatyrko and Y. Hattori
    • Organizer
      10th Prague Topology Symposium
    • Place of Presentation
      Prague (Czeko)
    • Year and Date
      20060800
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Lagrangian submanifolds with totally geodestic foliation in CP^n2006

    • Author(s)
      M. Kimura
    • Organizer
      Honam Mathematical Society, Annual Meeting
    • Place of Presentation
      韓国
    • Year and Date
      20060600
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Additive and product theorems for ind2006

    • Author(s)
      V. Chatyrko and Y. Hattori
    • Organizer
      2006 International Conference on Topology and its Applications
    • Place of Presentation
      Aegion (Greece)
    • Year and Date
      20060600
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] There is no upper bound of small transfinite compactness degree in metrizable spaces2006

    • Author(s)
      V. Chatyrko and Y. Hattori
    • Organizer
      2006 International Conference on Topology and its Applications
    • Place of Presentation
      Aegion (Greece)
    • Year and Date
      20060600
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Lawson topology of the space of formal balls and the hyperbolic subbase2006

    • Author(s)
      Y. Hattori and H. Tsuiki
    • Organizer
      2006 International Conference on Topology and its Applications
    • Place of Presentation
      Aegion (Greece)
    • Year and Date
      20060600
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Lagrangian submanifolds with totally geodestic foliation In CP2006

    • Author(s)
      M. Kimura
    • Organizer
      Honam Math. Soc., Annual Meeting
    • Place of Presentation
      Korea
    • Year and Date
      20060600
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] There is no upper bound of small transfinite compactness degree in metrizable spaces2006

    • Author(s)
      V. Chatyrko, Y. Hattori
    • Organizer
      2000 Internat. Conf. on Topology and its Applications
    • Place of Presentation
      Aegion (Greece)
    • Year and Date
      20060600
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Lawson topology of the space of formal balls and the hyperbolic subbase2006

    • Author(s)
      Y. Hattori, T. Tsuiki
    • Organizer
      2000 Internat. Conf. on Topology and its Applications
    • Place of Presentation
      Aegion (Greece)
    • Year and Date
      20060600
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Some remarks on generalized inverse *-semigroups2006

    • Author(s)
      T. Imaoka and T. Iigai
    • Organizer
      京都大学数理解析研究所研究集会「代数, 言語, 計算システムにおけるアルゴリズム問題」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      20060200
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Finite semigroups and decidability of amalgamation bases for semigroups2006

    • Author(s)
      K. Shoji
    • Organizer
      京都大学数理解析研究所研究集会「代数, 言語, 計算システムにおけるアルゴリズム問題」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      20060200
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Some remarks on generalized inverse *-semigroups2006

    • Author(s)
      T. Imaoka, T. Iigai
    • Organizer
      Workshop on Algorithmic problems in algebra, languages and computation systems
    • Place of Presentation
      RIMS, Kyoto Univ
    • Year and Date
      20060200
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Upper bounds of small transfinite compactness degree in metrizable spaces2005

    • Author(s)
      V. Chatyrko and Y. Hattori
    • Organizer
      京都大学数理解析研究所研究集会「一般・幾何学的トポロジーと幾何学的群論」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      20051000
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Partitions of spaces by locally compact subspaces2005

    • Author(s)
      V. Chatyrko, Y. Hattori and H. Ohta
    • Organizer
      日本数学会総合分科会
    • Place of Presentation
      岡山大学
    • Year and Date
      20050900
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Lagrangian submanifolds with some foliation in a complex projective space2005

    • Author(s)
      M. Kimura
    • Organizer
      第52回幾何学シンポジウム
    • Place of Presentation
      福岡大学
    • Year and Date
      20050800
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] A generalization of Cartan hypersurfaces2005

    • Author(s)
      M. Kimura
    • Organizer
      Defferential Geometry and Physics
    • Place of Presentation
      Budapest (Hungary)
    • Year and Date
      20050800
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Lagrangian submanifolds with some foliation in a complex Projective space2005

    • Author(s)
      M. Kimura
    • Organizer
      The 52nd Symposium on Geometry
    • Place of Presentation
      Fukuoka Univ
    • Year and Date
      20050800
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Topologies of spaces of formal balls in metric spaces2005

    • Author(s)
      Y. Hattori and H. Tsuiki
    • Organizer
      20th Summer Conference on Topology and its Applications
    • Place of Presentation
      Denison University Ohio (U.S.A.)
    • Year and Date
      20050700
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Topologies of spaces of formal balls in metric spaces2005

    • Author(s)
      Y. Hattori, H. Tsuiki
    • Organizer
      20th Summer conf. on Topology and its Appl
    • Place of Presentation
      Denion Univ., Ohio (USA)
    • Year and Date
      20050700
    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] Algebras, languages, computations and their applications2007

    • Author(s)
      K. Shoji
    • Total Pages
      154
    • Publisher
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
  • [Book] Algorithmic problem in algebra, languages and computation systems2006

    • Author(s)
      K. Shoji
    • Total Pages
      163
    • Publisher
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より

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Published: 2010-02-04  

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