Let $\mathbb{Z}$ be the D367: Set of integers.
The set of euclidean integers with respect to $N \in \{ 1, 2, 3, \ldots \}$ is the D11: Set
\begin{equation}
\mathbb{Z}^N
= \prod_{n = 1}^N \mathbb{Z}
\end{equation}
▶ | D5179: Set of euclidean natural numbers |