2004 Fiscal Year Final Research Report Summary
Combinatorial semigroup theory and its applications
| Project/Area Number |
15540029
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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 | Shimane University |
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Principal Investigator |
SHOJI Kunitaka Shimane University, Mathematics, Professor, 総合理工学部, 教授 (50093646)
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| Co-Investigator(Kenkyū-buntansha) |
IMAOKA Teruo Shimane University, Mathematics, Professor, 総合理工学部, 教授 (60032603)
MIWA Takuo Shimane University, Mathematics, Professor, 総合理工学部, 教授 (60032455)
FUJITA Kene-tsu Kunma University, Engineering, Associate Professor, 工学部, 助教授 (30228994)
UEDA Akira Shimane University, Mathematics, Associate Professor, 総合理工学部, 助教授 (70213345)
OZAKI Manabu Shimane University, Mathematics, Associate Professor, 総合理工学部, 助教授 (80287961)
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| Project Period (FY) |
2003 – 2004
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| Keywords | semigroup / group / amalgamation Problem / topological space / Fibre homotopy / λcalculus / valuation ring / Iwakawa module |
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| Research Abstract |
(1)Amalgamation problems for groups are strongly connected with word problems for groups, Especially, through amalgamation products of groups。 Consequently, many word problems for groups have been solved and many nice results have been brought by making use of amalgamation products of groups。
However, it is not too much to say that the situation for semigroups changes totally。 Actually, amalgams of groups are always embeddable in a group。 But amalgams of semigroups are not always embeddable in a semigroup。 M.Sapir proved negatively the amalgamation problem of semigroups asking fo "Does there exist an algorithm to decide whether or not an amalgam of finite semigroups are embeddable in a finite semigroup"。 Moreover、M.Sapir and T.E.Hall study the decidability pr@blem of "Does there exist an algorithm to decide whether or not a finite semigroup is an amalgamation base for all the semigroups. However, it is left unsolved. Investing the problem, we obtained another proof of Okninski and Putch
… More
a's theorem for finite inverse semigroups. Furthermore、we give a sufficient condition for regular semigorups to be an amalgamation base for all the semigroups.
(2)From a point view of topology, we construct frame work of fiber homotopy groups of continuous mapping and study fibre ANR property of mappings between stratifirable spaces
(3)From a point view of mathematical logic, we investigate rewriting systems and translations of λμ-calculus. From a point view of Utility computation modeling, we show the existence of exterior modeling for free λμ-calculus and study confluence of free λμ-calculus and relationship between free λμ-calculus and C-monoids. From a point view of algebraic algorithm, we study R-ideals of Dubrovin valuation rings with central finite dimensional Simple Artinian ring as a quotient ring. To clarify relationship between Iwasawa modules and computations of Galois groups, we investigate relationship between Z_p-extensions and Galois groups and obtain a generalization of Iwasawa theorem and some results on Greenberg's conjecture. Less
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