2009 Fiscal Year Final Research Report
Study of Noetherian local rings in commutative algebra
| Project/Area Number |
19540060
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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 | Osaka Electro-Communication University |
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Principal Investigator |
NISHIMURA Jun-ichi Osaka Electro-Communication University, 工学部, 教授 (00025488)
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| Co-Investigator(Kenkyū-buntansha) |
SAKATA Sadahisa 大阪電気通信大学, 医療福祉工学部, 教授 (60175362)
YAMAHARA Hideo 大阪電気通信大学, 工学部, 准教授 (30103344)
MIYAZAKI Mitsuhiro 京都教育大学, 教育学部, 准教授 (90219767)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 環論 |
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| Research Abstract |
Construction of big Cohen-Macaulay modules over mixed characteristic local rings : The conjectures on finitely generated modules over Noetherian local rings asked by H.Bass and M.Auslander are called "Homological Conjectures". Many commutative algebraists have studied on this subject. M.Hochster showed that the existence of big Cohen-Macaulay modules implies the conjectures and succeeded to show the existence over equal characteristic local rings. We have got the result over mixed characteristic local rings.
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