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Definition D608
Integer multiplication operation

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 $$\mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}, \quad [(a, b)] [(c, d)] = [(a c + b d, a d + b c)]$$

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 $$\mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}, \quad [(a, b)] [(c, d)] = [(a \cdot c + b \cdot d, a \cdot d + b \cdot c)]$$
Children
 ▶ Rational multiplication operation