Date of Award
Thesis - Restricted
Master of Science (MS)
In his paper, "On Quasi-decompositions of Torsion Free Abeilian Groups" , 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.
Perham, Faustine L., "On Torsion Free Modules and Their Quasi-Endomorphism Rings" (1965). Master's Theses (1922-2009) Access restricted to Marquette Campus. 2172.