Definition:Field of Quotients/Definition 3

Definition
Let $D$ be an integral domain.

A quotient field of $D$ is a pair $(F,\iota)$ 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 $\varphi = \bar\varphi \circ \iota$

Also see

 * Equivalence of Definitions of Quotient Field