Project/Area Number  09640071 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Algebra

Research Institution  Meiji University 
Principal Investigator 
GOTO Shiro Meiji University, School of Science and Technology, Professor, 理工学部, 教授 (50060091)

CoInvestigator(Kenkyūbuntansha) 
阿原 一志 明治大学, 理工学部, 講師 (80247147)
YAMAGISHI Kikumichi Himeji Dokkyo University, Faculty of General Education, Professor, 一般教育学部, 助教授 (10200601)
服部 晶夫 明治大学, 理工学部, 教授 (80011469)
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)
NAKAMURA Yukio Meiji University, School of Science and Technology, Lecturer, 理工学部, 講師 (00308066)
SHIMODA Yasuhiro Kitasato University, Center of General Education, Associate Professor, 一般教育総合センター, 助教授 (10226277)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,000,000 (Direct Cost : ¥3,000,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1997 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  Buchsbaum ring / CohenMacaulay ring / Gorenstein ring / canonical module / Rees algebra / associated graded ring / form ring / local cohomology / Buchsbaun環 / Cohenmacaulay環 / Gorenstein環 / 正準加群 / Rees代数 / 随伴次数環 / S^1manifold / ヒルベルト類体 / CohenMacaulay環 / 随半次数環 
Research Abstract 
What I want to do in my research is to study certain ringstructures (such as Buchsbaumness, CohenMacaulayness, or Gorensteinness) of Rees algebras associated to ideals in Noetherian local rings, from the viewpoint of the corresponding properties of their associated graded rings. In [G1] I gave a characterization for the Rees algebras associated to mprimary ideals of minimal multiplicity in CohenMacaulay 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 ainvariant conjecture raised by KorbNakamura, concerning a question on the CohenMacaulayness 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 c
… More
riterion for the associated graded rings of mprimary 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 noncommutative algebra and performed ajoint research with Kenji Nishida. Someof the results will appear in [GN1, GN2]. [G_1]S.Goto.Buchsbaumness in Rees algebras associated to ideals of minimal multiplicity.Joural of Algebra(to appaer) [G_2]S.Goto.CohenMacaulayness versus negatiyity of ainvariants in Rees algebras associated to ideals of minimal multiplicity,the Proceedings of the conference in honor of David Buchsbaum(to appaer) [GN_1]S.Goto.and K.Nisihida.Catenarity in modulefinite algebras.Proc.Amer.Math.Soc.(to appaer) [GN_2]S.Goto and K.Nisihida.Minimal injective resoulutions of CohenMacaulay isolated singularities.Archiv der Mathemati(to appaer) [Y]K.Yamagishi,The associated graded medules of Buchsbaum modules with respect to m・primary ideals in equiIinvariant case.Joural of Algebr(to appaer) Less
