Definition:Multiplicative Group of Positive Rational Numbers

Definition
The multiplicative group of positive rational numbers $\left({\Q_{> 0}, \times}\right)$ is the set of (strictly) positive rational numbers under the operation of multiplication.

Also see

 * Strictly Positive Rational Numbers under Multiplication form Countably Infinite Abelian Group

Thus rational multiplication is:


 * Well-defined on $\Q_{> 0}$
 * Closed on $\Q_{> 0}$
 * Associative on $\Q_{> 0}$
 * Commutative on $\Q_{> 0}$
 * The identity of $\left({\Q_{> 0}, \times}\right)$ is $1$
 * Each element of $\left({\Q_{> 0}, \times}\right)$ has an inverse.