notes / Studies in Algebra and Group Theory / chapter 17: Further Topics in Algebra / Commutative Ring Theory

17.2 Euclidean Domains

Definition 17.2.1 (Euclidean domain). An integral domain is a Euclidean domain (ED) if there exists a function (the Euclidean norm) such that for any with , there exist with

Example 17.2.1 (Euclidean domains).

with .
(for a field) with .
The Gaussian integers with .
The Eisenstein integers where , with .