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.

Included in

Mathematics Commons

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