Let $\mathbb{Z}$ be the D367: Set of integers.
Let $+$ be the D637: Natural number addition operation.
Let $\cdot$ be the D638: Natural number multiplication operation.
The integer multiplication operation is the D554: Binary operation
\begin{equation}
\mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}, \quad
[(a, b)] [(c, d)] = [(a c + b d, a d + b c)]
\end{equation}