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.

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