1998 Fiscal Year Final Research Report Summary
Study of Rees algebras and form rings
| Project/Area Number |
09640071
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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 | Meiji University |
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Principal Investigator |
GOTO Shiro Meiji University, School of Science and Technology, Professor, 理工学部, 教授 (50060091)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Yukio Meiji University, School of Science and Technology, Lecturer, 理工学部, 講師 (00308066)
YAMAGISHI Kikumichi Himeji Dokkyo University, Faculty of General Education, Professor, 一般教育学部, 助教授 (10200601)
SHIMODA Yasuhiro Kitasato University, Center of General Education, Associate Professor, 一般教育総合センター, 助教授 (10226277)
INATOMI Akira Meiji University, School of Science and Technology, Professor, 理工学部, 教授 (20061872)
TSUSHIMA Ryuji Meiji University, School of Science and Technology, Associate Professor, 理工学部, 助教授 (20118764)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Buchsbaum ring / Cohen-Macaulay ring / Gorenstein ring / canonical module / Rees algebra / associated graded ring / form ring / local cohomology |
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| Research Abstract |
What I want to do in my research is to study certain ring-structures (such as Buchsbaumness, Cohen-Macaulayness, or Gorensteinness) of Rees algebras associated to ideals in Noetherian local rings, from the view-point of the corresponding properties of their associated graded rings. In [G1] I gave a characterization for the Rees algebras associated to m-primary ideals of minimal multiplicity in Cohen-Macaulay local rings (A, m) to be Buchsbauxn rings, in terms of the corresponding property of the associated graded rings and the extended Rees algebras as well. As a byproduct of this research I constructed a counterexample to the negative a-invariant conjecture raised by Korb-Nakamura, concerning a question on the Cohen-Macaulayness in Rees algebras. Igave a lecture about the examples in the International Conference on Commutative Algebra in honor of David Buchsbaum (the third period, Genova) in Italy ([G2]). Also, K.Yarnagishi [Y] generalized the techniques in [G1], and gave a striking criterion for the associated graded rings of m-primary ideals in Buchsbaum local rings to be Buchsbaum, in terms of the Buchsbaum invariant. He gave a talk about this criterion at the International Conference on Commutative Algebra in honor of David Buchsbaum (the first period, Catania) in Italy, which I organized as one of the organizers. I am also interested in non-commutative algebra and performed ajoint research with Kenji Nishida. Someof the results will appear in [GN1, GN2].
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