Uniquely Euclidean norm

This article defines a property that can be evaluated for a Euclidean norm on a commutative unital ring

Definition

A Euclidean norm on a commutative unital ring is termed uniquely Euclidean if it satisfies the following: for any two elements in the ring, there is only one possibility for the corresponding remainder (there may be multiple possibilities for the quotient, if the ring is not an integral domain).