Date

2016

Department or Program

Mathematics

Primary Wellesley Thesis Advisor

Alexander Diesl

Abstract

We introduce Anderson's and Livingston's definition of a zero-divisor graph of a commutative ring. We then redefine their definition to include looped vertices, enabling us to visualize nilpotent elements. With this new definition, we examine the algebraic and graph theoretic properties of different types of Artinian rings, culminating in an algorithm that determines the corresponding Artinian rings to a zero-divisor graph. We also will explore and develop an algorithm for a specific case of Artinian rings, and we will conclude by examining the uniqueness of zero-divisor graphs.

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