Date of Award

Summer 1965

Degree Type

Thesis - Restricted

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Swokowski, Earl

Abstract

In his paper, "On Quasi-decompositions of Torsion Free Abeilian Groups" [7], 1 James D. Reid obtains in his main theorem a one-to-one correspondence between what he defines to be the quasi-decompositions of a group and the decompositions of its quasi-endomorphism ring. He considers the groups to be torsion free Abelian subgroups of a fixed rational vector space, In the following discussion prompted by a suggestion at the conclusion of Reid's article, we let M be a fixed vector space over a division ring D and consider submodules M2 of M where M2 is an R-module, R a sub-integral domain of D. By extending Reid's definitions to the category of modules, we are able to establish results for modules similar to those obtained for groups.

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