Mathematical Sciences: Rings with Approximation Property andQuestions About The Special Linear Group Over Regular Rings

数学科学：具有近似性质的环以及关于正则环上的特殊线性群的问题

• 批准号: 8805872
• 负责人: Christel Rotthaus
• 金额: $ 3.9万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard 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=8805872&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Rings; Approximation; Property

This research deals with two problems in commutative algebra. The first is to determine if rings with the approximation property are excellent. The second problem is related to the Bass-Quillen conjecture. The study of the geometric properties of rings involves the analysis of the commutative rings that arise in algebraic geometry. This project concerns approximating regular local rings by smooth algebras. While interesting in its own right, it also has application to the Bass-Quillen conjecture on projective modules.

本文研究交换代数中的两个问题。第一个是确定具有逼近性质的环是否优秀。第二个问题与Bass-Quillen猜想有关。环的几何性质的研究涉及到对代数几何中产生的交换环的分析。这个项目涉及用光滑代数逼近正则局部环。虽然它本身很有趣，但它也适用于投影模上的Bass-Quillen猜想。