Mathematical Sciences: The Structure of Abelian Groups - A Unified Approach

这项研究涉及一种统一的方法， 有挠、无挠和混合的分类问题 阿贝尔群 首席研究员将继续 学习公理3和等价定理， 无扭转和混合情况。 他还在试验 提炼纯净的概念，使技术最初旨在 更普遍有用的阿贝尔群的特定类。 这个项目是在阿贝尔群理论的一般领域 并涉及阿贝尔群的分类。 虽然有限阿贝尔群的分类已经被 一个世纪以来， 阿贝尔群仍然难以捉摸。 这项研究涉及到这个古老的 无限交换群的分类问题 通过逻辑和分析的新工具来接近。

This research is concerned with a unified approach to classification problems for torsion, torsion-free, and mixed abelian groups. The principal investigator will continue studying Axiom 3 and equivalence theorems in an effort to access the torsion-free and mixed cases. He is also experimenting with refined concepts of purity to make techniques originally aimed at specific classes of abelian groups more universally useful. 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.