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

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。

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.