ThmDex – An index of mathematical definitions, results, and conjectures.
 ▼ Set of symbols ▼ Alphabet ▼ Deduction system ▼ Theory ▼ Zermelo-Fraenkel set theory ▼ Set ▼ Binary cartesian set product ▼ Binary relation ▼ Map ▼ Operation ▼ N-operation ▼ Binary operation ▼ Enclosed binary operation ▼ Groupoid ▼ Ringoid ▼ Semiring ▼ Ring ▼ Multiplicative group ▼ Multiplicative monoid ▼ Multiplicative semigroup ▼ Multiplicative groupoid ▼ Multiplicative binary operation ▼ Natural number multiplication operation ▼ Integer multiplication operation
Definition D609
Rational multiplication operation

Let $\mathbb{Q}$ be the D368: Set of rational numbers.
Let $\cdot$ be the D608: Integer multiplication operation.
The rational multiplication operation is the D554: Binary operation $$\mathbb{Q} \times \mathbb{Q} \to \mathbb{Q}, \quad [(a, b)] [(c, d)] = [(a c, b d)]$$

Let $\mathbb{Q}$ be the D368: Set of rational numbers.
Let $\cdot$ be the D608: Integer multiplication operation.
The rational multiplication operation is the D554: Binary operation $$\mathbb{Q} \times \mathbb{Q} \to \mathbb{Q}, \quad [(a, b)] [(c, d)] = [(a \cdot c, b \cdot d)]$$
Children
 ▶ D610: Real multiplication operation