Classification of Abelian Groups & Module

该奖项支持研究某些类别的有限秩不可分解巴特勒群，在离散估值环上的co-纯粹不可分解模块，以及在拉回环上的coherent生成的不可分解模块的结构。 包括的是按不变式分类的项目。 特别注意将致力于确定有限的，驯服的，或野生的表示类型为每个类考虑。 无限维Z-表示将被用来研究围绕实现（非阿贝尔）群作为域的自同构群的问题。 这个项目是在阿贝尔群理论的一般领域。 它关注的是阿贝尔群的分类和这方面的知识应用到其他领域。 虽然有限阿贝尔群的分类在世纪以来已经被很好地理解，但无限阿贝尔群的分类仍然是难以捉摸的。 这项研究涉及这个老问题的分类无限阿贝尔群接近新的工具，从逻辑和拓扑。

This award supports research on the structure of certain classes of finite rank indecomposable Butler groups, co-purely-indecomposable modules over a discrete valuation ring, and finitely generated indecomposable modules over pullback rings. Included are projects for classification by invariants. Particular attention will be devoed to determining finite, tame, or wild representation type for each class considered. Infinite dimensional Z-representations will be used to investigate problems revolving around realizations of (nonabelian) groups as automorphism groups of fields. This project is in the general area of abelian group theory. It is concerned with the classification of abelian groups and the application of this knowledge to other areas. Although the classification of finite abelian groups has been well understood for a century, the classification of infinite abelian groups remains elusive. This research involves this old problem of classification of the infinite abelian groups approached by new tools from logic and topology.