Author ORCID Identifier
Date of Award
8-2024
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics and Statistics
First Advisor
Yongwei Yao
Second Advisor
Florian Enescu
Third Advisor
Mark Grinshpon
Fourth Advisor
Zhongshan Li
Abstract
This dissertation explores the use of the Frobenius endomorphism to detect the regularity of a ring within the framework of commutative algebra. In commutative local rings of prime characteristic, invariants such as the Hilbert-Kunz multiplicity, F-signature, and Frobenius Betti numbers have been shown to detect regularity. Polstra and Smirnov [PS21] showed that the Frobenius Euler characteristic can be used to determine regularity for the class of strongly F-regular rings. Here, we extend their results by relaxing the condition of strong F-regularity. We show that the Frobenius Euler characteristic can detect regularity for rings with sufficient F-splitting and for rings that are Cohen-Macaulay.
DOI
https://doi.org/10.57709/37395360
Recommended Citation
Wilson, Ryan, "Regularity Criteria via the Frobenius Euler Characteristic." Dissertation, Georgia State University, 2024.
doi: https://doi.org/10.57709/37395360
File Upload Confirmation
1