Mathematical Sciences: Residual Intersections and Linkage ofCohen-Macaulay Ideals

这项研究是在交换代数的一般领域。 这个项目关注的是 在剩余交集下保持理论特性。 此外，主要研究者将发现必要的和 一个理想在的联结类中的充分条件 完全切除 交换环研究的一个目标是分类 具有某些性质的理想。其中许多结果具有 应用于代数几何中的问题和对应物。 一个有趣的话题是，一个理想是否与 另一个理想与第二个理想中的任何一个都相同 #21453;的属性，或者在多大程度上这样做。后一个问题是 这个项目的主要关注点。

This research is in the general area of commutative algebra. The project is concerned with the question of which ring theoretic properties are preserved under residual intersections. In addition, the principal investigator will find necessary and sufficient conditions for an ideal to be in the linkage class of a complete interesection. One goal in the study of commutative rings is to classify ideals having certain properties. Many of these results have applications to problems and counterparts in algebraic geometry. One interesting topic is whether an ideal related by linkage to another ideal shares any of the second ideals interesting properties, or to what extent it does so. This latter problem is the primary concern of this project.