Mathematical Sciences: Primary Decompositions and Ajoints of Ideals

数学科学：理想的初级分解和联合

• 批准号: 9623085
• 负责人: Irena Swanson
• 金额: $ 6万
• 依托单位: New Mexico State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623085&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Primary; Decompositions; Ajoints

Swanson 96-23085 This proposal supports the work of Professor I. Swanson to work on problems in commutative algebra. She intends to study how, in Noetherian rings of prime characteristic, primary deomposiiton varies with Frobenius powers. She also hopes to develop algorithms for calculating adjoints and cores when the ring is not two dimensional. This research is on the boundary between commutative algebra and algebraic geometry. Both fields arose from the classical problem of studying mathematical objects defined in the plane by the simplest of equations, namely polynomials. Today, the fields use methods not only from algebra, but also from analysis and topology, and conversely are extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.

斯旺森96-23085 这一建议支持了I教授的工作。斯旺森工作的问题交换代数。她打算研究如何，在诺特环的主要特征，小学deomposition变化与弗罗贝纽斯权力。她还希望开发出计算伴随和核的算法，当环不是二维的时候。 本文的研究是在交换代数与代数几何的边界上进行的。这两个领域产生于经典的问题，研究数学对象定义在平面上的最简单的方程，即多项式。今天，这些领域不仅使用代数方法，而且还使用分析和拓扑学方法，相反，这些领域广泛使用。 此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人学等不同领域都很有用。