Research on the Hilbert functions in local rings

2014 Fiscal Year Final Research Report

• Project/Area Number: 25800020
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Yamaguchi University
• Principal Investigator: OZEKI Kazuho 山口大学, 理工学研究科, 講師 (70445849)
• Project Period (FY): 2013-04-01 – 2015-03-31
• Keywords: 可換環論 / ヒルベルト函数 / ヒルベルト係数 / Sally加群 / コーエン・マコ―レイ環 / ブックスバウム環

Outline of Final Research Achievements

The purpose of this research is to explore the behavior of the Hilbert functions of ideals in a commutative Noetherian local ring. The representative of this research gave the following results.
1. Research on the Hilbert coefficients of parameter ideals: The purpose of this research is to explore the relationship between the first Euler characteristics and the homological degrees of modules. We also investigate the first and the second Hilbert coefficients of parameters in connection with the homological torsions of modules.
2. Research on the structure of the Sally modules: The purpose of this research is to study the structure of the Sally module of maximal ideal with rank at most three in a Cohen-Macaulay local ring.

Free Research Field

代数学