| Project/Area Number |
09440017
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 |
IMAOKA Teruo Shimane University, Interdisciplinary Faculty of Science and Engineering, Professor, 総合理工学部, 教授 (60032603)
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| Co-Investigator(Kenkyū-buntansha) |
ITO Masami Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (50065843)
KONDO Michio Shimane University, Interdisciplinary Faculty of Science and Engineering, Associate Professor, 総合理工学部, 助教授 (40211916)
SHOJI Kunitaka Shimane University, Interdisciplinary Faculty of Science and Engineering, Professor, 総合理工学部, 教授 (50093646)
KOBAYASHI Yuji Toho University, Faculty of Science, Professor, 理学部, 教授 (70035343)
KATSURA Masashi Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (80065870)
NEHANIV C. 会津大学, コンピュータ理工学部, 教授 (10254054)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥5,900,000 (Direct Cost: ¥5,900,000)
Fiscal Year 1999: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1998: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1997: ¥3,000,000 (Direct Cost: ¥3,000,000)
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| Keywords | semigroup / representation / amalgamation / formal language / rewriting system / free monoid / automata / computation / semigroup / representation / amalgamation / formal language / rewriting system / free monoid / automata / computation |
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| Research Abstract |
The main results of this project are as follows :
(1)The class of generalized inverse [*-]semigroups has the strong amalgamation property.
(2)The transitive representations of a generalized inverse *-semigroup is characterized by using right ω-cosets.
(3)We obtained the necessary and sufficient conditions for that a completely 0-simple semigroup is a special amalgamation base.
(4)The decision problem whether or not a finite semigroup has representation extension property is decidable.
(5)Several properties and a characterization of the shuffle residual of a language are obtained. For example, conditions for the existence of maximal languages whose shuffle residual equals a given language are obtained.
(6) We obtained concrete descriptions of the free algebras in several varieties given by language structures equipped with the operations of reversal, concatenation, shuffle and others.
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