Definition:Coprime/Euclidean Domain

Definition
Let $\left({D, +, \times}\right)$ be a Euclidean domain.

Let $U \subseteq D$ be the Group of Units of $D$.

Let $a, b \in D$ such that $a \ne 0_D$ and $b \ne 0_D$

Let $d = \gcd \left\{{a, b}\right\}$ be the greatest common divisor of $a$ and $b$.

Then $a$ and $b$ are coprime, or relatively prime, if $d \in U$.

That is, two elements of a Euclidean domain are coprime iff their greatest common divisor is a unit of $D$.