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半加群のホモロジー代数

Research Project

Project/Area Number 05640109
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionKobe University

Principal Investigator

高橋 典大  神戸大学, 工学部, 教授 (00031295)

Co-Investigator(Kenkyū-buntansha) 田村 直之  神戸大学, 工学部, 助教授 (60207248)
田畑 稔  神戸大学, 工学部, 講師 (70207215)
角田 譲  神戸大学, 工学部, 教授 (50031365)
南部 隆夫  神戸大学, 工学部, 教授 (40156013)
中桐 信一  神戸大学, 工学部, 教授 (20031148)
Project Period (FY) 1993
Project Status Completed (Fiscal Year 1993)
Budget Amount *help
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1993: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordssemiring / semimodule / lattice / injective / frame / cancellatuie / R-regular / quasi-order
Research Abstract

単位元1εをもつ半環S上のS-半加群Aについて.次の結果を得た。
1.2-半環S(1=1+1)上のS-半加群Aは常にある完備束I(A)に埋め込まれることを示し,Sが可除2-半環で,AがframeのときAがinjectvieになることを証明した。また,この可除2-半環の基本的構造を明らかにし,その典型的ないくつかの例を作った。
2.S-半加群のS-関係Rから定義されるS-関係
S(R)={(x,y)|x+u=y+v for some(u,v)εR}がAの擬順序であることを証明し,これまで知られていたAの基本的な部分半加群:G(A),C(A),R(A),s(A)及び商半加群c(A),σ(A),τ(A),K(A)がこのS(R)からすべて導びかれることを示し,それらの間の基本的関係を明らかにした。

Report

(1 results)
  • 1993 Annual Research Report
  • Research Products

    (6 results)

All Other

All Publications (6 results)

  • [Publications] M.Takahashi: "Injective semimodules over a 2-semiring" Kobe J.of Math.10. 59-70 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] S.Nakagiri: "Review of Japanese work of the last ten years on identifiability in distributed parameter systems" Inverse Problems. 9. 143-191 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] J.M.Jeong: "Structural operators and semigroups associated with functional differantial equations in Hilbert space" Osaka J.Math.30. 365-395 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] T.Nambu: "Robustness of feedback control systems of parabolic type against perturbations to an ellrptic operator" Journal of Differential Equations. 110 to appear. (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] M.Tabata: "Decay of solutions to the mixed problem with the periodicity bounday condition for the linearized Boltzmann system" Commun.in Particl Differential Equations. 18. 1823-1846 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] M.Tabata: "Decay of solutions to the cansly problem for the linearized Boltzmann equation with the some external-force Potential" Japan J.Indust.Appl.Math.10. 237-253 (1993)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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