2003 Fiscal Year Final Research Report Summary
| Project/Area Number |
13640034
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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 | Tokyo Metropolitan University |
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Principal Investigator |
KAWASAKI Takeshi Tokyo Metropolitan University, Graduate School of Science, assistant, 理学研究科, 助手 (40301410)
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| Co-Investigator(Kenkyū-buntansha) |
TERAO Hiroaki Tokyo Metropolitan University, Graduate School of Science, professor, 理学研究科, 教授 (90119058)
KURANO Kazuhiko Meiji University, school of soi. and teohv, professor, 理工学部, 教授 (90205188)
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| Project Period (FY) |
2001 – 2003
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| Keywords | Cohen-Macaulay ring / excellent ring / Rees algebra / dualzing complex / Cousin complex |
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| Research Abstract |
Let A be a Noetherian ring and I an ideal of A. If I is of positive height and the Rees algebra R(I) of I is Cohen-Macaulay, then R(I) is called an Arithmetic Cohen-Macaulayfication of A. We give a necessary and sufficient condition for A to have an arithmetic Macaulayfication. That is, A has an arithmetic Macaulayfication if and only if A satisfies
(C1)A is universally catenary ;
(C2)all the formal fiber of any localization of A are Cohen-Macaulay ;
(C3)the Cohen-Macaulay locus of any finitely generated A-algebra B is open in Spec B ;
(QU)for any pair of prime ideals p ⊂ q, ht q = ht q/p + ht p ;
(UM)A has no embedded primes.
In consequence of this result, we show that A is a homomorphic image of a Cohen-Macaulay ring if and only if A satisfies (C1)-(C3) and
(CD)A has a codimension function.
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