2001 Fiscal Year Final Research Report Summary
Homological structure and representation of Noetherian algebras
| 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)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Noetherian algebra / Gorenstein Algebra / Gorenstein dimension / dualizing module / order |
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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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