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

数学科学：阿贝尔群的结构 - 统一方法

• 批准号: 9208199
• 负责人: Paul Hill
• 金额: $ 9.87万
• 依托单位: Auburn University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9208199&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Structure; Abelian; Groups

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.

这项研究涉及扭转群、无扭转群和混合阿贝尔群分类问题的统一方法。 主要研究者将继续研究 Axiom 3 和等价定理，以研究无扭转和混合情况。 他还正在尝试精炼的纯度概念，以使最初针对特定类别的阿贝尔群的技术变得更加普遍有用。 该项目属于阿贝尔群理论的一般领域，涉及阿贝尔群的分类。 尽管有限阿贝尔群的分类一个世纪以来已被广泛理解，但无限阿贝尔群的分类仍然难以捉摸。 这项研究涉及无限阿贝尔群的分类这个老问题，通过逻辑和分析的新工具来解决。