Studies in Commutative Algebra and Computational Algebra

交换代数和计算代数研究

• 批准号: 9801413
• 负责人: Wolmer Vasconcelos
• 金额: $ 11.5万
• 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: 1998
• 资助国家: 美国
• 起止时间: 1998-06-01 至 2002-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9801413&HistoricalAwards=false
• 关键词: Studies; Commutative; Algebra; Computational

Vasconcelos, 98-01413 Abstract Vasconcelos This award supports research in commutative algebra, algebraic geometry and computational algebra. It is centered on the development of a new series of numerical signatures of rings and algebras, the so-called homological degrees, that play in local rings and arbitrary algebras a role similar to Castelnuovo--Mumford's regularity in graded structures. It will also emphasize the algebraization (particularly Cohen-Macaulayness and normality) of blowup algebras---Rees algebras of ideals and modules and tangent and secant algebras---and the examination of algebras associated to commuting sets of elements of Lie algebras, the computation of rings of invariants of connected groups and algebras of combinatorial interest. Commutative algebra is broadly concerned with solutions of structured sets of polynomial and analytic equations, and the study of pathways to methods and algorithms that facilitate the efficient processing in large scale computations with such data. These equations often arise internally in the construction of new geometric structures or in domains of applications, such as control and coding theory and robotic motion. A mathematically focused approach is required in order to beat the complexity in problems of interest.

Vasconcelos，98-01413 摘要 Vasconcelos 该奖项支持交换代数，代数几何和计算代数的研究。它集中在 发展了一系列新的数字签名的环和代数，所谓的 同调度，局部环和任意代数中对策 一个类似于Castelnuovo的角色--Mumford在分级结构中的规则性。 它还将强调 代数化（特别是Cohen-Macaulayness 和正规性）的blowup代数-里斯 代数的理想和模块和切线和割线代数-和检查代数相关联的交换集的元素李代数，计算环的不变量的连接群 和代数的组合兴趣。 交换代数广泛地关注结构化集合的解， 多项式和解析方程，并研究途径的方法和 这些算法有助于在大规模计算中对这些数据进行有效处理。这些方程经常出现在新的几何结构或应用领域的建设内部，如控制和编码理论和机器人运动。为了克服感兴趣的问题的复杂性，需要一种以数学为重点的方法。