\begin{definition}[Definition:Field of Quotients/Definition 1]
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
:$(3): \quad \forall z \in F: \exists x \in D, y \in D_{\ne 0}: z = \dfrac {\map \iota x} {\map \iota y}$
\end{definition}