Definition:Field of Quotients/Definition 2

Definition
Let $D$ be an integral domain.

Let $F$ be a field.

$F$ is the quotient field of $D$ :
 * $(1): \quad$ There exists an ring monomorphism $\iota : D \to F$
 * $(2): \quad$ If $K$ is a field with $\iota \left({D}\right) \subset K \subset F$, then $K = F$.

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