Complex Extensions, An Introduction

Introduction

In basic number theory, we introduced the gaussian integers, which can be thought of as integer points in the complex plane. These complex integers multiply and divide like traditional integers. They also factor uniquely into primes.

In this section we will explore the gaussian integers in more detail, and examine some additional complex extensions, i.e. other lattices in the complex plane. Some of these extensions exhibit unique factorization into primes; some do not.

This is not a complete exploration of negative quadratic extensions, which requires some background in algebraic number theory.