Definition:Field of Quotients/Definition 1

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
 * $(3): \quad \forall z \in F: \exists x \in D, y \in D_{\neq 0}: z = \dfrac {\iota \left({x}\right)} {\iota \left({y}\right)}$

Also see

 * Equivalence of Definitions of Quotient Field