| Project/Area Number |
11640020
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Shinshu University |
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Principal Investigator |
NISHIDA Kenji Shinshu University, Science, Professor, 理学部, 教授 (70125392)
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| Co-Investigator(Kenkyū-buntansha) |
NINOMIYA Yasushi Shinshu University, Science, Professor, 理学部, 教授 (40092887)
MUKAI Juno Shinshu University, Science, Professor, 理学部, 教授 (50029675)
IWANAGA Yasuo Shinshu University, Education, Professor, 教育学部, 教授 (80015825)
FUJITA H. University of Tsukuba, Mathematical Science, Instructor, 数学系, 講師 (60143161)
HANAKI Akihide Shinshu University, Science, Assistant Professor, 理学部, 助教授 (50262647)
山崎 愛一 京都大学, 総合人間学部, 助教授 (10283590)
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| Project Period (FY) |
1999 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2001: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2000: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1999: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | Noetherian algebra / Gorenstein Algebra / Gorenstein dimension / dualizing module / order / アルティン多元環 / ネータ環 / バス予想 / 有限入射次元 / 完全加群 |
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| Research Abstract |
We consider a theory of non-commutative Noetherian algebras as commutative ring theory. Mainly, we consider an algebra which is finitely generated as a module over a commutative Noetherian ring. We define a Gorenstein algebra by the Cousin complex and give a characterization of a Gorenstein algebra by the Bass number. Indeed, the fact concerning Bass numbers holds completely similar to that of commutative rings. We extend the results due to R. Y. Sharp to our algebras, namely, under some assumption, we give a category equivalence between the category of finite modules of finite injective dimension and that of finite modules of finite protective dimension. We give a criterion that a module over an order or artin algebra is a dualizing modulen and apply it to a Cohen-Macaulay isolated singularities. We study a global dimension of a tiled oreder. Especially, we give a theory to deal with a tiled order having a large global dimension.
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