Mathematical Sciences: Projective Modules Over Affine Rings

这个项目的主要研究者将继续研究仿射代数上的投射模的结构及其在仿射代数理想理论中的应用。具体地说，将研究投射模的抵消性质和仿射簇的集论完全交问题。首席调查员还将考虑嵌入仿射变种的问题。这项研究涉及代数几何和交换代数的问题。这是目前数学中一个非常活跃的领域。这一结果可能会对这一地区的发展方向产生重大影响。

The principal investigator on this project will continue studying the structure of projective modules over affine algebras and their application to ideal theory of affine algebras. Specifically, cancellation properties of projective modules and the question of set-theoretic complete intersection for affine varieties will be investigated. The principal investigator will also consider embedding questions for affine varieties. This research is concerned with questions involving algebraic geometry and commutative algebra. This is a very active area of mathematics at present. The outcome could have a substantial impact on the directions in which this area is heading.