Project/Area Number  09640038 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Algebra

Research Institution  SHIMANE UNIVERSITY 
Principal Investigator 
庄司 邦孝 島根大, 総合理工学部, 教授 (50093646)
UEDA Akira SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING ASSOCIATED PROFESSOR, 総合理工学部, 助教授 (70213345)

CoInvestigator(Kenkyūbuntansha) 
MIWA Takuo SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING PROFESSOR, 総合理工学部, 教授 (60032455)
ENDO Michiro SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING ASSOCIATED PROFESSOR, 総合理工学部, 助教授 (40211916)
KIKKAWA Michihiko SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING PROFESSOR, 総合理工学部, 教授 (70032430)
KAMIYA Noriaki SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING ASSOCIATED PROFESSOR, 総合理工学部, 助教授 (90144691)
IMAOKA Teruo SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING PROFESSOR, 総合理工学部, 教授 (60032603)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,100,000 (Direct Cost : ¥3,100,000)
Fiscal Year 1998 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1997 : ¥1,900,000 (Direct Cost : ¥1,900,000)

Keywords  combinatorial semigroup theory / automaton / algorithm / amalgamation base / valuation ring / universal algebra / loop / representation / 組合せ半群論 / オートマトン / アルゴリズム / 融合基 / 付値環 / 一般代数 / ループ / 表現 / 組合せ半群 / 一般代数系 / 融合 / 正則半群 / ホップ代数 / 非可換付値環 
Research Abstract 
1. Decision problem whether or not a finite semigroup has a certain property (P) has been studied by many mathematicians, and Spair and Guba proved that for many properties (P) the decision problem is undecidable. Concerning this problem, Shoji proved that there exists an algorithm to decide whether or not a finite semigroup has the representation extension property. Furthermore, shoji proved the following results (1) For completely 0simple semigroup S, the following are equivalent. (i) S is a special amalgamation base. (ii) S is either left absolutely flat or right absolutely flat. (iii) S satisfies either left annihilator condition or right annihilator condition. (2) For finite commutative semigroup T, the following are equivalent. (i) T is a completely special amalgamation base. (ii) T is completely amalgamation base. (iii) T is Eseparable. 2. As applications of combinatorial semigroup theory we obtained the following results. (1) Imaoka investigated about representations of generalized inverse *semigroups. (2) Ueda studied about Prufer orders in simple Artinian rings. In particular, Ueda characterized branched and unbranched prime ideals of Prufer orders. (3) Kondo gave an axiom system of a nonlinear 4valued logic , whose Lindenbaum algebra is the de Morgan algebra with implication. (4) Miwa obtained a new characterization of superparacompact spaces. Miwa also defined new covering properties and studied invariance and inverse invariance under various maps of these covering properties. (5) Kikkawa introduced the algebraic concept of projectivity of a Lie triple algebra and investigated about properties of Lie algebra of projectivity.
