# Definition:Quotient Field/Definition 2

## 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
$(3): \quad$ If $K$ is a field with $\iota \left({D}\right) \subset K \subset F$, then $K = F$.

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