1996 Fiscal Year Final Research Report Summary
Study on algebras and their representations
| Project/Area Number |
06302002
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 総合 |
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| Research Field |
Algebra
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
AKIBA Tomoharu Kyoto Univ., Integrated Human Studies, Professor, 総合人間学部, 教授 (60027670)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIDA Kenji Nagasaki Univ., General Education, Profssor, 教養部, 教授 (70125392)
WATANABE Keiichi Tokai Univ., Science, Professor, 理学部, 教授 (10087083)
GOTO Shiro Meiji Univ., Science and enjineering, Professor, 理工学部, 教授 (50060091)
YAMAGATA Kunio Tsukuba Univ., Motheiratics, Associate Professor, 数学系, 助教授 (60015849)
YOSHINO Yuji Kyoto Univ., Integrated Human Studies, Associate Professor, 総合人間学部, 助教授 (00135302)
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| Project Period (FY) |
1994 – 1996
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| Keywords | local rings / Cohen-Macaulay modules / singularities / discrepancy / Rees algebras / Frobenius algebras / Bass orders / Zariski's problem |
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| Research Abstract |
To afford financial assistance to all the integrated studies on algebra based on the theory of rings and their representations, we summoned representative researchers of this area in Japan as the members of this project. In order to contribute the investigation on algebra or more widely on mathematics itself, we had planned several symposia on the subject and had tried to make every researcher in this area available to communicate with other researchers in Japan and also abroad. To be more concrete, under the agreement of all the members, we organized the symposium on commutative rings, the symposium on ring theory and the symposium on the representation theory of algebras. Worthy of special mention is that we organized the second Japan-China symposium on ring theory (1995) and the International symposium on commutative algebra (1996). We had taken these opportunities to exchange informations and to make joint studies with the foreign researchers who visited Japan.
Under the present project, Yoshino had continued his study on Cohen-Macaulay modules and got several new results on the lifting problems and on the problem of matrix factorizations. Watanabe succeeded to give a clear explanation on the relationship between the theory of tight closure in positive characteristic and the theory of discrepancy in nul charactersitic and broke new ground to the theory of singularities. Goto had obtained several new results on the Cohen-Macaulay property of Rees algebras when the local rings have rather small deviations. Yamagata had kept researching on Frobenius algebras and developed a new theory of socle deformation for self-injective algebras. Nishida clarified the structures of Bass orders and primary orders of finite representation type. Nagata obtained a new result on Zariski's problem related with the 14th problem of Hilbert.
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