Mathematical Sciences: Invariants and Endomorphisms of Groups and Modules

该奖项将支持对结构的研究， 各类有限和可数秩无挠 阿贝尔群 巴特勒集团的类将被分类 直到（准或近）-同构的不变量在 Baer和乌尔姆不变量的传统。 各种应用 代数的其他领域，如有限的表示， 多重拉回上的偏序集和可重构生成模 戒指也将被考虑。 该项目是在阿贝联集团的一般地区 理论，并与阿贝尔分类有关 组 虽然有限交换群的分类 世纪以来， 无限阿贝尔群仍然是难以捉摸的。 本研究 涉及到了无穷大的分类这个老问题 阿贝尔群接近的新工具，从逻辑和 分析.

This award will support the study of the structure of various classes of finite and countable rank torsion-free abelian groups. Classes of Butler groups will be classified up to (quasi or near)-isomorphism by invariants in the tradition of Baer and Ulm invariants. Various applications to other areas of algebra, such as representations of finite posets and finitely generated modules over multiple pullback rings will also be considered. This project is in the general area of abelian group theory and is concerned with the classification of abelian groups. 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 analysis.