## All Theses

#### Title

Conductors and Rings with Shared Ideals

8-2022

Thesis

#### Degree Name

Master of Science (MS)

#### Department

Mathematical Sciences

Dr. jim Coykendall

Dr. Michael Burr

Dr. Hui Xue

#### Abstract

Given an additive subgroup $I$ of a field $K$, we define the colon ideal (I:I) = {\alpha \in K: \alpha I \subseteq I}. We then use this to construct collections of rings with shared ideals and explore relationships between these concepts and the complete integral closure.

COinS