Definition:Field of Quotients/Definition 3

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 $\iota: D \to F$
 * $(2): \quad$ $F$ satisfies the following universal property:
 * For every field $E$ and for every ring monomorphism $\varphi : D \to E$, there exists a unique field homomorphism $\bar \varphi : F \to E$ such that $\varphi = \bar\varphi \circ \iota$