Mathematical Sciences: Applications of Linkage

数学科学：联动的应用

• 批准号: 8802888
• 负责人: Matthew Miller
• 金额: $ 5.55万
• 依托单位: University of South Carolina at Columbia
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802888&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Applications; Linkage

The technique of linkage has been instrumental in attacking a diverse group of problems in commutative algebra. Professors Kustin and Miller will concentrate in this research mainly on the aspects of the theory that involve the interplay of linkage with the structure of finite free resolution of perfect ideals, putting particular emphasis on the multiplicative structures supported on these resolutions. They will also extend this study to the more flexible relation of residual intersection, so that previous techniques can be extended to a wider class of algebras. They are particularly interested in Rees algebras, and algebras defined by sequences and matrices of indeterminates. Applications to determination of rationality of Poincare series and the computation of certain K-groups are expected.

联动技术在解决交换代数中的各种问题方面发挥了重要作用。 库斯汀和米勒教授将在这项研究中主要集中于涉及与完美理想的有限自由解析结构的相互作用的理论方面，特别强调这些解析所支持的乘法结构。 他们还将这项研究扩展到更灵活的残差交集关系，以便以前的技术可以扩展到更广泛的代数类别。 他们对里斯代数以及由不定数序列和矩阵定义的代数特别感兴趣。 预计可应用于庞加莱级数合理性的确定和某些 K 群的计算。