1998 Fiscal Year Final Research Report Summary
COMBINATORIAL SEMIGROUP THEORY AND ITS APPLICATIONS
| Project/Area Number |
09640038
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | SHIMANE UNIVERSITY |
|---|
Principal Investigator |
UEDA Akira SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING ASSOCIATED PROFESSOR, 総合理工学部, 助教授 (70213345)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KAMIYA Noriaki SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING ASSOCIATED PROFESSOR, 総合理工学部, 助教授 (90144691)
KIKKAWA Michihiko SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING PROFESSOR, 総合理工学部, 教授 (70032430)
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)
IMAOKA Teruo SHIMANE UNIVERSITY FACULTY OF SCIENCE AND ENGINEERING PROFESSOR, 総合理工学部, 教授 (60032603)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| Keywords | combinatorial semigroup theory / automaton / algorithm / amalgamation base / valuation ring / universal algebra / loop / representation |
|---|
| 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 0-simple 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 E-separable.
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 non-linear 4-valued 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.
|
