Date of Award

Spring 1-1-2014

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Katherine Stange

Second Advisor

David Grant

Third Advisor

Robert Tubbs

Fourth Advisor

Eric Stade

Fifth Advisor

Franck Vernerey

Abstract

In this thesis we find that all imaginary n-quadratic fields with n>3 have class number larger than 1 and therefore cannot be Euclidean. We also examine imaginary triquadratic fields, presenting a complete list of 17 imaginary triquadratic fields with class number 1, and classifing many of them according to whether or not they are norm-Euclidean. We find that at least three of these fields are norm-Euclidean, and at least five are not.

Included in

Mathematics Commons

Share

COinS