# Field of fractions

In abstract algebra, the **field of fractions** of an integral domain is the smallest field in which it can be embedded. The construction of the field of fractions is modeled on the relationship between the integral domain of integers and the field of rational numbers. Intuitively, it consists of ratios between integral domain elements.

The **semifield of fractions** of a commutative semiring with no zero divisors is the smallest semifield in which it can be embedded.