Mathematical Sciences: Abelian Groups and Modules Over Commutative Domains

本文研究阿贝尔群中的一些问题 理论和交换域上的模理论。 巴特勒集团的几个问题将被考虑，以及 群的挠积问题。校长 调查人员还将调查模块的估值 域.对一般域上的模的深入研究将 特别强调的是， 矩阵的投影维数为1。 这个项目有它的根在阿贝尔群的理论。 阿贝尔群是具有交换 乘法运算它们出现在一些领域， 数学这项研究有两个基本目标。一个人可能有 交换代数的含义;第二个涉及使用 研究阿贝尔群的逻辑技巧。

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.