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.

Author ORCID Identifier

0000-0002-9404-5159

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