Definition:Field of Quotients/Definition 2

Definition
Let $R$ be an integral domain.

Let $F$ be a field.

$F$ is the quotient field of $R$ :
 * $(1): \quad$ There exists an embedding $\iota : R \to F$
 * $(2): \quad$ If $K$ is a field with $\iota(R) \subset K \subset F$, then $K=F$.

That is, the quotient field of an integral domain $R$ is the smallest field containing $R$ as a subring.