Mathematical Sciences: Invariants for Abelian Groups

研究了有限秩无扭阿贝尔群和有限赋值p群的不变量问题。这个项目的成功完成将会得到一个包含Warfield群的混合阿贝尔群的完备不变量集。其他研究领域包括与有限部分有序集合的向量空间表示的联系，在其自同态环上作为平面模的无扭阿贝尔群的结构，以及e模。本课题属于阿贝尔群论的一般领域，涉及阿贝尔群的分类。虽然有限阿贝尔群的分类已经被很好地理解了一个世纪，无限阿贝尔群的分类仍然是难以捉摸的。本研究涉及到无穷阿贝尔群的分类这一老问题，并用新技术加以解决。

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.