Term of Award
Summer 2017
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Saeed Nasseh
Committee Member 1
Alina Iacob
Committee Member 2
Jimmy Dillies
Abstract
The purpose of this thesis is to introduce and illustrate some of the deep connections between commutative and homological algebra. We shall cover some of the fundamental definitions and introduce several important classes of commutative rings. The later chapters will consider a particular class of rings, the \emph{fiber product}, and, among other results, show that any Gorenstein fiber product is precisely a one dimensional hypersurface. It will also be shown that any Noetherian local ring with a (nontrivially) decomposable maximal ideal satisfies the Auslander-Reiten conjecture. To conclude, generalizations of results by Takahashi and Atkins-Vraciu shall be presented.
Recommended Citation
VandeBogert, Keller, "Fiber Products in Commutative Algebra" (2017). Electronic Theses and Dissertations. 1608.
https://digitalcommons.georgiasouthern.edu/etd/1608
Research Data and Supplementary Material
No
