ABSTRACT
In Chapters 1 through 4 we considered the quadratic fieldsK = Q( √ D) and
the rings of integers R = O(√D), and we kept our discussion as elementary as possible while still proving interesting results. But this consideration was just the tip of an iceberg. Our aim in this chapter is to indicate how these results generalize. The field of mathematics that these generalize to is known as algebraic number theory. As a matter of historical fact, our development here parallels the development of algebraic number theory. Historically, quadratic fields were considered first, and their investigation motivated the investigation of more general algebraic number fields.
