Date of Award
8-2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
School of Mathematical and Statistical Sciences
Committee Chair/Advisor
James Coykendall
Committee Member
Michael Burr
Committee Member
Ryann Cartor
Committee Member
Robert Dicks
Committee Member
Hui Xue
Abstract
This dissertation will explore factorization within orders in a number ring. By far the most well-understood of these orders are rings of algebraic integers. We will begin by examining how certain types of subrings may relate to the larger rings in which they are contained. We will then apply this knowledge, along with additional techniques, to determine how the elasticity in an order relates to the elasticity of the full ring of algebraic integers. Using many of the same strategies, we will develop a corresponding result in the rings of formal power series. Finally, we will explore a number of additional cases, including several explicit examples of orders of interest.
Recommended Citation
Moles, Grant, "Relating Elasticity and Other Multiplicative Properties Among Orders in Number Fields and Related Rings" (2024). All Dissertations. 3750.
https://open.clemson.edu/all_dissertations/3750
Author ORCID Identifier
0000-0002-9404-5159