Date of Award
4-30-2018
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics and Statistics
First Advisor
Yongwei Yao
Second Advisor
Florian Enescu
Third Advisor
Zhongshan Li
Fourth Advisor
Mariana Montiel
Abstract
This dissertation investigates the characterization of F-rationality. Much work has been done to characterize F-rationality. Here, we will assume that the underlying ring is commutative and Noetherian with unity of prime characteristic p. Juan Vélez was able to prove many results on rings that are closely related to Cohen-Macaulay rings via canonical modules. Thus, we studied his paper and we tried to improve his results. Using Karen Smith's result in her dissertation work, we were able to obtain different approaches to prove some similar results of Juan Vélez. This allows us to further analyze the relationship between F-rationality and canonical modules. Eventually, we obtained a few more interesting characterizations of F-rationality when R is reduced F-finite Cohen-Macaulay.
DOI
https://doi.org/10.57709/12001877
Recommended Citation
Ng, Shuenn, "Characterizing F-rationality of Cohen-Macaulay Rings via Canonical Modules." Dissertation, Georgia State University, 2018.
doi: https://doi.org/10.57709/12001877