Norm-Euclidean ring of integers

This article defines a property that can be evaluated for a ring of integers in a number field

Definition

The ring of integers of a number field is termed norm-Euclidean if it is a Euclidean domain where the norm is given by the usual norm in a ring of integers. In other words, the norm is the product of all algebraic conjugates, counted to the correct multiplicity.

Since the norm in a ring of integers is multiplicative, norm-Euclidean rings possess multiplicative Euclidean norms.

Relation with other properties

Weaker properties

• Euclidean ring of integers