Research on the powers of modules and their saturation

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400038
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Chiba University
• Principal Investigator: Nishida Koji 千葉大学, 統合情報センター, 教授 (60228187)
• Co-Investigator(Renkei-kenkyūsha): KURANO Kazuhiko 明治大学, 理工学研究科, 教授 (90205188)
• Research Collaborator: FUKUMURO Kosuke ; INAGAWA Taro ; KUME Hirofumi ; ISOBE Ryotaro ; KUMASHIRO Shinya
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 可換環 / 記号的べき乗 / 記号的リース代数

Outline of Final Research Achievements

We studied the saturation of the Rees algebra R(M) of a module M over a local ring R. If M is an R-module appearing as the cokernel of a homomorphism of finitely generated free R-modules, putting suitable assumption on f, we could describe an acyclic complex concretely which gives an R-free resolution for a homogeneous component of the saturation of R(M). We considered the ideals of R as the objects of our research. In order to place emphasis on the point of view that ideals are submodules of rank one free modules, we avoided putting the assumption that the ideals are prime, which is common in the study on symbolic Rees algebras. As a consequence, we could generalize the Huneke's criterion on the Noetherian property of the symbolic Rees algebras of prime ideals in 3-dimensional regular local rings, and we found an interesting application.

Free Research Field

可換環論