Definition:Multiplicative Group of Rational Numbers
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Definition
The multiplicative group of rational numbers $\struct {\Q_{\ne 0}, \times}$ is the set of rational numbers without zero under the operation of multiplication.
Also see
Thus rational multiplication is:
- Well-defined on $\Q_{\ne 0}$
- Closed on $\Q_{\ne 0}$
- Associative on $\Q_{\ne 0}$
- Commutative on $\Q_{\ne 0}$
- The identity of $\struct {\Q_{\ne 0}, \times}$ is $1$
- Each element of $\struct {\Q_{\ne 0}, \times}$ has an inverse.