| Project/Area Number |
62540047
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | Hyogo University of Teacher Education |
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Principal Investigator |
YANAGIHARA Hiroshi Hyogo University of Teacher Education, 学校教育学部, 教授 (00033803)
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| Co-Investigator(Kenkyū-buntansha) |
MATSUYAMA Hiroshi Hyogo University of Teacher Education, 学校教育学部, 助教授 (80028266)
KOIKE Satoshi Hyogo University of Teacher Education, 学校教育学部, 助教授 (60161832)
WATANABE Kinji Hyogo University of Teacher Education, 学校教育学部, 助教授 (20004468)
NOMURA Yasutoshi Hyogo University of Teacher Education, 学校教育学部, 教授 (20029630)
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| Project Period (FY) |
1987 – 1988
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| Project Status |
Completed (Fiscal Year 1988)
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| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1988: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1987: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | finite group / involutory automorphism / weakly normal ring / seminormal ring / Hopf algebra / involutory automorphism / blowing-up、jet finite group / blowing-up, jet |
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| Research Abstract |
This research project was planned mainly for commutative ring theory and the term of reserch was two years of 1987 and 1988. In this period the head investigator, Yanagihara, obtained three results, one of which is concerned with short exact sequences of cocommutative Hopf algebras and a generalization of a corresponding result for hyperalgebras by T.Shudo. The other two results by him involve seminormal local rings and weakly normal rings. E.Davis gave a chariacterzation of reduced seminormal local rings of dimension 1 by multiplicity and embedded dimension in 1978. Our result is a generalization of this to the higher dimensional cases. As for weakly normal rings we datermined weakly normal domains whose weakly normal underrings are always integrally closed. Moreover a new characterization of weakly normal rings was obtained. Koike, who is one of investigators, obtained some interestingresults in the field of real algebraic geometry. Matsuyama and Watanabe also got interesting results on group theory and partial differential equations, respectively.
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