Definition:Field of Quotients/Definition 2

Definition
Let $D$ be an integral domain.

A field of quotients of $D$ is a pair $\struct {F, \iota}$ such that:
 * $(1): \quad F$ is a field
 * $(2): \quad \iota: D \to F$ is a ring monomorphism
 * $(3): \quad$ If $K$ is a field with $\iota \sqbrk D \subset K \subset F$, then $K = F$.

That is, the field of quotients of an integral domain $D$ is the smallest field containing $D$ as a subring.

Also see

 * Equivalence of Definitions of Field of Quotients