Mathematical Sciences: Computer Assisted Studies in Commutative Algebra

数学科学：交换代数的计算机辅助研究

• 批准号: 8902117
• 负责人: Wolmer Vasconcelos
• 金额: $ 10.88万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902117&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Computer; Assisted; Studies

This project is directed at studying Cohen-Macaulay rings and algebras, and effectively computing their invariants. Its aims are to uncover and extend the role of Koszul homology in the structure theory of Cohen-Macaulay singularities; to investigate the structure of the algebras of linear type; to examine the equations of symbolic power algebras; to study the invariants and singularities of commuting varieties of Lie algebras and their representations; and to develop methods and algorithms that allow for very large scale computations in commutative algebra. This research is in the general area of commutative algebra and the computer-aided computational aspects of this field. There is a growing interest in using computers to answer theoretical questions. This project makes serious use of both the theory and practice of symbolic calculations to solve real problems in commutative algebra.

本项目旨在研究Cohen-Macaulay环和代数，并有效地计算它们的不变量。其目的是揭示和扩展kozul同源性在Cohen-Macaulay奇点结构理论中的作用；研究线性型代数的结构；考察符号幂代数的方程；研究李代数交换变簇的不变量和奇异性及其表示；并且开发方法和算法来允许在交换代数中进行大规模的计算。本研究是在交换代数的一般领域和该领域的计算机辅助计算方面。人们对用计算机回答理论问题越来越感兴趣。本项目认真运用符号计算的理论和实践来解决交换代数中的实际问题。