Mathematical Sciences: Invariants for Abelian Groups

数学科学：阿贝尔群的不变量

• 批准号: 8802062
• 负责人: David Arnold
• 金额: $ 9.44万
• 依托单位: New Mexico State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802062&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Invariants; Abelian; Groups

This research is concerned with the study of invariants for torsion-free abelian groups of finite rank and finite valuated p- groups. Successful completion of this project will result in a complete set of invariants for a large class of mixed abelian groups that includes the class of Warfield groups. Other areas of investigation include the connection with vector space representations of finite partially ordered sets, the structure of torsion-free abelian groups that are flat as modules over their endomorphism ring, and E-modules. 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 with new techniques.

本研究涉及的是研究的不变量， 有限秩和有限值p- 组该项目的成功完成将导致 一类混合交换的不变量的完备集 群，包括沃菲尔德群类。的其他领域 研究包括与向量空间的联系 有限偏序集的表示，结构 作为模平坦的无挠阿贝尔群 自同态环和E-模。 这个项目是在阿贝尔群理论的一般领域 并关注阿贝尔群的分类。 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 无限阿贝尔群的分类问题， 用新的技术接近。