---
tag: 0F2PTGX1A2
kind: concept
name: Field of fractions
aliases: [fraction-field, quotient-field]
msc: [13B30]
sources:
  - url: https://en.wikipedia.org/wiki/Field_of_fractions
    locator: lead section
same_as:
  wikidata: Q774579
  wikipedia: Field of fractions
---

## Summary

The field of fractions of an integral domain is the smallest field that contains it.
Its elements are the fractions $a/b$ with $b \neq 0$.
The rational numbers are the field of fractions of the integers.
The [[definition of the field of fractions|0VF11ZTTMD]] gives the construction.