Definition:Pairwise Coprime/Euclidean Domain

Definition
Let $\struct {D, +, \times}$ be a Euclidean domain.

A subset $S \subseteq D$ is pairwise coprime (in $D$) :
 * $\forall x, y \in S: x \ne y \implies x \perp y$

where $x \perp y$ denotes that $x$ and $y$ are coprime.

Also see

 * Definition:Coprime Elements of Euclidean Domain