Publication Date

Summer 7-28-2020

Abstract

An order is a subring of the ring of integers of an algebraic extension, Peruginelli and Zanardo classified the lattices of orders with prime index inside te ring of integers of quadratic extensions of the rational numbers. The lattices are quite striking and have different layered structure depending on whether the prime is inert, split, or ramified. This thesis considers the orders which have prime power index inside the Gaussian integers. This is a nice generalization of the work of Peruginelli and Zanardo, and succeeds in a few classifications of specific instances of orders derived from inert primes.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Dr. Janet Vassilev

Second Committee Member

Dr. Hongnian Huang

Third Committee Member

Dr. Alexandru Buium

Language

English

Keywords

Lattice, Prime Splitting Type, Quadratic Orders

Document Type

Thesis

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