Definition:Field of Quotients

Definition
Let $D$ be an integral domain.

Let $F$ be a field.

Also defined as
It is common to define a field of quotients simply as a field $F$, instead of a pair $\struct {F, \iota}$. The embedding $\iota$ is then implicit.

The field of quotients can also be defined to be the explicit construction from Existence of Field of Quotients.

Also see

 * Equivalence of Definitions of Field of Quotients
 * Existence of Field of Quotients, where it is shown that the field of quotients always exists
 * Field of Quotients is Unique, which justifies the use of the definite article

Generalizations

 * Definition:Total Ring of Fractions
 * Definition:Localization of Ring