Mathematical Sciences: Abelian Groups and Modules Over Commutative Domains

本文主要研究交换整环上的交换群论和模理论中的问题。将考虑有关Butler群的几个问题，以及关于群的扭积的问题。首席调查员还将调查估值领域的模块。我们将对一般整环上的模进行深入的研究，特别强调当商的域具有射影维度1时的情形。这个项目源于交换群的理论。阿贝尔群是具有交换乘法运算的代数对象。它们出现在数学的许多领域。这项研究有两个基本推动力。一种可能对交换代数有影响；第二种涉及在阿贝尔群研究中使用逻辑技巧。

This research is concerned with problems in abelian group theory and in the theory of modules over commutative domains. Several problems on Butler groups will be considered, as well as problems on the torsion product of groups. The principal investigator will also investigate modules over valuation domains. An in-depth study of modules over general domains will be undertaken with special emphasis on the situation when the field of quotients has projective dimension 1. This project has its roots in the theory of abelian groups. Abelian groups are algebraic objects having a commutative multiplicative operation. They arise in a number of areas of mathematics. This research has two basic thrusts. One may have implications for commutative algebra; the second involves the use of logical techniques in the study of abelian groups.