Date of Award
Doctor of Philosophy (PhD)
Mathematics and Statistics
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.
Ng, Shuenn, "Characterizing F-rationality of Cohen-Macaulay Rings via Canonical Modules." Dissertation, Georgia State University, 2018.