Mathematical Sciences: Abelian Groups and Modules Over Commutative Domains

本文研究了交换域上的阿贝尔群论和模理论中的一些问题。本文将考虑关于Butler群的几个问题，以及群的扭转积问题。首席研究员还将调查评估域上的模块。对一般域上的模块进行深入研究，特别强调商域具有射影维数1的情况。这个项目植根于阿贝尔群理论。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目的。一个可能对交换代数有启示；第二个涉及到在阿贝尔群的研究中使用逻辑技术。

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.