Classification of Abelian Groups & Module

阿贝尔群的分类

• 批准号: 9400958
• 负责人: David Arnold
• 金额: $ 5万
• 依托单位: Baylor University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-15 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400958&HistoricalAwards=false
• 关键词: Classification; Abelian; Groups; & Module

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.

该奖项支持对某些有限秩不可分解Butler群、离散赋值环上的余纯不可分解模以及拉回环上的有限生成不可分解模的结构的研究。其中包括按不变量分类的项目。将特别注意为所考虑的每一类确定有限、驯服或狂野的表示类型。无限维Z-表示将被用来研究围绕着(非交换)群作为场的自同构群的实现的问题。这个项目属于交换群论的一般领域。它涉及阿贝尔群的分类以及这一知识在其他领域的应用。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一古老的问题，新的工具从逻辑和拓扑学的角度探讨了这一问题。