Definition:Field of Rational Functions

Definition
Let $K$ be a field, and let $K \left[{x}\right]$ be the integral domain of polynomial forms on $K$.

Let $K \left({x}\right)$ be the set of rational functions on $K$, i.e.:
 * $K \left({x}\right) = \left\{{\forall f \in K \left[{x}\right], g \in K \left[{x}\right]^*: \dfrac {f \left({x}\right)} {g \left({x}\right)}}\right\}$

where $K \left[{x}\right]^* = K \left[{x}\right] \setminus \left\{{\text{the null polynomial}}\right\}$.

Then $K \left({x}\right)$ is the field of rational functions on $K$.

Also see

 * Field of Rational Functions is Field