\begin{definition}[Definition:Pairwise Coprime/GCD Domain]
Let $\struct {D, +, \times}$ be a GCD domain.
A subset $S \subseteq D$ is '''pairwise coprime (in $D$)''' {{iff}}:
:$\forall x, y \in S: x \ne y \implies x \perp y$
where $x \perp y$ denotes that $x$ and $y$ are coprime.
\end{definition}