Project/Area Number 
13640023

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Algebra

Research Institution  Shimane University 
Principal Investigator 
SHOJI Kunitaka Shimane University, Mathematics, Professor, 総合理工学部, 教授 (50093646)

CoInvestigator(Kenkyūbuntansha) 
FUJITA Kenetsu Shimane University, Information, Assistant Professor, 総合理工学部, 助教授 (30228994)
MIWA Takuo Shimane University, Mathematics, Professor, 総合理工学部, 教授 (60032455)
IMAOKA Teruo Shimane University, Mathematics, Professor, 総合理工学部, 教授 (60032603)
OZAKI Manabu Shimane University, Mathematics, Assistant Professor, 総合理工学部, 助教授 (80287961)
UEDA Akia Shimane University, Mathematics, Assistant Professor, 総合理工学部, 助教授 (70213345)
近藤 通朗 島根大学, 総合理工学部, 助教授 (40211916)

Project Period (FY) 
2001 – 2002

Project Status 
Completed (Fiscal Year 2002)

Budget Amount *help 
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2001: ¥2,000,000 (Direct Cost: ¥2,000,000)

Keywords  semigroup / amalgam / algorithm / fibre / homotopy / rewriting system / caluculus / Iwasawa theory / レトラクト / 岩沢不変 / 群 / 融合問題 / 語の問題 / 自由融合積 / メンバーズシップ問題 / 不値環 
Research Abstract 
(1) There is no solution of the problem whether or not there exists an algorithm to decide if a finite semigroup is an amalgamation base for all semigroups. On the other hand, it is known that a semigroup which is an amalgamation base for all semigroups always has the representation extension property. In this project, we prove that there exists an algorithm to decide if a finite semigroup has the representation extension property. Also, it is known that a completely 0simplesemigroup with the representation extension property is an amalgamation base for all semigroups. However, we can construct by the software "Mathematic" an example of a finite regular semigroup with the representation extension property and without being an amalgamation base for all semigroups. Moreover, we prove that there exists an algorithm to decide if a finite semigroup is left absolutely flat. The result will appear in a forthcoming paper. (2) We prove that a finite semigroup which is an amalgamation for all finite semigroups has the representation extension property. As a consequence, we decide the structure of finite bands which is an amalgamation for all finite semigroups. (3) We give another proof of Okininski and Putcha's theorem on finite inverse semigroup, which is a natural extension of B.Neumann's result on group. (4) We show that the construction of λ μmodels can be given by the use of a fixed point operator and the GodelGentzen translation. (5) We study the fibrewise homotopy, fibrewise fibration and fibrewise cofibration. (6) Let p be an odd prime number. By using Iwasawa theory we construct cyclotopic fields whose maximal real subfields have class group with arbitrarily large prank and a conductor with only four prime factors.
