Divisor Graph and Factorization Type

Author

Masoumeh SoleimaniFollow

Date of Award

5-2024

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Industrial Engineering

Committee Chair/Advisor

Professor James Coykendall

Committee Member

Dr. Matt Macauley

Committee Member

Dr. Hui Xue

Abstract

In this project, we examine some natural ideal conditions and show how graphs can be defined that give a visualization of these conditions. We examine the interplay between the multiplicative ideal theory and the graph-theoretic structure of the associated graph. In this research, we associate a graph in a natural way with the divisors of a commutative ring. ii

Comments

we endeavor at first to generalize these notions to a more general setting, and then, inspired by this work, we will look at “factorization types” for elements in monoids and domains. This project is outlined as follows. First, some definitions, theorems, and examples are listed. Proofs that provide useful insight for our purposes will be included, but for other results, we will merely include a citation to a work containing the proof. In addition, well-known or minor results, which will be used later, will be presented. All rings are assumed to be commutative with identity unless otherwise stated. Chapter 1 contains foundational results about the ring theory and graph theory. Chapter 2 contains some results about divisor graphs. Chapter 3 is about factorization as well as key examples and proofs.

Recommended Citation

Soleimani, Masoumeh, "Divisor Graph and Factorization Type" (2024). All Theses. 4287.
https://open.clemson.edu/all_theses/4287