\begin{definition}[Definition:Field of Quotients/Definition 3]
Let $D$ be an integral domain.
A '''field of quotients''' of $D$ is a pair $\struct {F, \iota}$ where:
:$(1): \quad$ $F$ is a field
:$(2): \quad$ $\iota : D \to F$ is a ring monomorphism
:$(3): \quad$ it 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 $\varphi = \bar \varphi \circ \iota$
\end{definition}