Definition:Field of Rational Numbers

Definition
The field of rational numbers $\left({\Q, + \times, \le}\right)$ is the set of rational numbers under the two operations of addition and multiplication, totally ordered by $\le$.

When the totally ordering $\le$ is subordinate or irrelevant in the context in which it is used, $\left({\Q, + \times}\right)$ is usually seen.

Also see

 * Rational Numbers form Totally Ordered Field

Thus:
 * $\left({\Q, +}\right)$ is the additive group of rational numbers
 * $\left({\Q_{\ne 0}, \times}\right)$ is the multiplicative group of rational numbers
 * The zero of $\left({\Q, + \times}\right)$ is $0$
 * The unity of $\left({\Q, + \times}\right)$ is $1$.