Date of Award
5-2024
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematical Sciences
Committee Chair/Advisor
Dr. James Coykendall, Committee Chair
Committee Member
Dr. Ryann Cartor
Committee Member
Dr. Robert Dicks
Abstract
This project explores elasticity in quadratic rings of integers, specifically, those of the form Z[pω] where p is a rational prime which remains prime in Z[w]. For these rings, we establish an upper bound on the elasticity which is attained in many cases. We also prove that this upper bound is an equality in the case when the ring of integers is a unique factorization domain. During this process, we also prove theorems about the class group of quadratic rings of integers and develop a useful method for calculating a constant similar to the Davenport constant.
Recommended Citation
Kettinger, Jared, "Elasticity of Orders in Quadratic Rings of Integers" (2024). All Theses. 4388.
https://open.clemson.edu/all_theses/4388