Mathematical Sciences: Invariants and Endomorphisms of Groups and Modules

这一奖项将支持对各类有限可数秩挠自由阿贝尔群的结构的研究。Butler群的类将按照Baer和Ulm不变量的传统被分类到(拟或接近)-同构。还将考虑在代数的其他领域的各种应用，例如有限偏序集的表示和多个拉回环上的有限生成模。本项目属于交换群论的一般领域，涉及交换群的分类。虽然有限阿贝尔群的分类已经被很好地理解了一个世纪，但无限阿贝尔群的分类仍然难以捉摸。这项研究涉及到无限阿贝尔群的分类这个古老的问题，这是从逻辑和分析的新工具所接近的。

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.