ABSTRACT
Some of the properties of extensions of fields are pointed out. Algebraic numbers and algebraic integers are defined. It is shown that the ring https://www.w3.org/1998/Math/MathML"> a K https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351023344/b6c68d68-1226-4347-aaa8-58dfe0c0d0a9/content/eq1561.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> of integers of an algebraic number field K is a Dedekind domain. We observe that an algebraic number field possesses an ‘integral basis’. The structure of the ring of integers of a quadratic number field is presented. The Diophantine equation x 2 + 2y 2 = n is solved. The chapter is concluded with a set of worked-out examples and exercises.
