2001 Fiscal Year Final Research Report Summary
Research of automatic structure which appear in algebras
| Project/Area Number |
10640030
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Naruto University of Education |
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Principal Investigator |
KOBAYASHI Shigeru Naruto University of Education, Teacher education, Associate professor, 学校教育学部, 助教授 (10195779)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIKAWA Tsuneo Osaka Institute of Technology, Technology, Associate Professor, 工学部, 助教授 (40268230)
YUTANI Hiroshi Naruto University of Education, Teacher education, Lecturer, 学校教育学部, 講師 (80200872)
MARUBAYASHI Hidetoshi Naruto University of Education, Teacher education, Professor, 学校教育学部, 教授 (00034702)
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| Project Period (FY) |
1998 – 2001
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| Keywords | Automaton / Local cohomology / Groebner basis / Torsion theory / Inverse semigroups / Valuation ring / Weyl algebras |
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| Research Abstract |
I researched automatic structure which appears in algebras.
(1) Automatic structure of semi-group theory.
There is a rational operation in semi-groups and generation D = J is filled in the equivalent relation of Green. It was able to divide into three types and we could obtain the structure.
(2) Automatic structure of ring theory.
Local cohomology of Weyl algebra can be calculated by using Groebner basis and Torsion theory. We obtained the algorithm to calculate extension of non-commutative valuation ring under some conditions. And another I researched automatic structure of number theory and logic.
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