Date of Award


Document Type


Degree Name

Master of Science (MS)


Industrial Engineering

Committee Chair/Advisor

Professor James Coykendall

Committee Member

Dr. Matt Macauley

Committee Member

Dr. Hui Xue


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


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.



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