Mathematical Sciences: Tight Closure and Absolute Integral Closures, Briancon-Skoda Theorems and Graded Rings

数学科学：紧闭包和绝对积分闭包、Briancon-Skoda 定理和分级环

• 批准号: 9413870
• 负责人: Ian Aberbach
• 金额: $ 5.99万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9413870&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Tight; Closure; Absolute

9413870 Aberbach This award supports research in commutative algebra. The principal investigator will explore the structure of the absolute integral closure of excellent local rings. He will also study the Cohen-Macaulayness of graded rings for ideals of higher analytic deviation. This research is concerned with a number of questions in commutative algebra and algebraic geometry. Algebraic geometry studies solutions of families of polynomial equations. One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring. This dual perspective creates a close connection between commutative algebra and algebraic geometry.

9413870 阿伯巴赫 该奖项支持交换代数的研究。 主要研究者将探索优秀局部环的绝对积分闭包的结构。 他还将研究科恩-麦考莱度分级环的理想较高的分析偏差。 本研究涉及交换代数和代数几何中的一些问题。 代数几何研究多项式方程族的解。 人们既可以研究解集的几何，也可以通过研究形成交换环的解集上的某些函数来代数地处理问题。 这种双重视角在交换代数和代数几何之间建立了密切的联系。