Definition:Field of Quotients/Definition 1

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

Also see

 * Equivalence of Definitions of Field of Quotients