Date of Award
8-2022
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
School of Mathematical and Statistical Sciences
Committee Chair/Advisor
James Coykendall
Committee Member
Hui Xue
Committee Member
Keri Sather-Wagstaff
Committee Member
Kevin James
Abstract
We will examine orders R in a number field K. In particular, we will look at how the generalized class number of R relates to the class number of its integral closure R. We will then apply this to the case when K is a quadratic field to produce a more specific relation. After this, we will focus on orders R which are half-factorial domains (HFDs), in which the irreducible factorization of any element α∈R has fixed length. We will determine two cases in which R is an HFD if and only if its ring of formal power series R[[x]] is an HFD. Finally, we will consider how these strategies may apply (or fail to apply) to more general results.
Recommended Citation
Moles, Grant, "The HFD Property in Orders of a Number Field" (2022). All Theses. 3851.
https://tigerprints.clemson.edu/all_theses/3851
Author ORCID Identifier
0000-0002-9404-5159