Date of Award
Fall 2009
Degree Type
Thesis
Degree Name
Master of Arts (MA)
Department
Mathematics
Advisor
Timothy Hsu
Subject Areas
Mathematics.
Abstract
This thesis studies the conditions under which certain U (G)-modules have integral dimension. Specifically, the paper explores the circumstances under which certain U (G)-modules are free modules. Two main theorems are proven for this endeavor. The first theorem takes the matrix representation A of a submodule N of a free left module M over an arbitrary ring R. The theorem states that if A can be put into reduced row echelon form, then N and M/N are both free left R-modules. The second theorem takes the matrix representation B of an arbitrary left R-module homomorphism T. If B can be put into reduced column echelon form, then Ker( T) is a free left R-module as well. The results of these theorems are well-known if R is a field or division ring. The results are also probably known for an arbitrary ring R , but there does not seem to be a readily accessible source in the standard literature.
Recommended Citation
Dharia, Sejal K., "Integral and non-integral dimension of modules over non-commutative rings." (2009). Master's Theses. Paper 3988.
http://scholarworks.sjsu.edu/etd_theses/3988