Editing Integral domain (section)

== Field of fractions ==
{{main|Field of fractions}}

The [[field of fractions]] ''K'' of an integral domain ''R'' is the set of fractions ''a''/''b'' with ''a'' and ''b'' in ''R'' and {{nowrap|''b'' ≠ 0}} modulo an appropriate equivalence relation, equipped with the usual addition and multiplication operations.  It is "the smallest field containing ''R''" in the sense that there is an injective ring homomorphism {{nowrap|''R'' → ''K''}} such that any injective ring homomorphism from ''R'' to a field factors through ''K''. The field of fractions of the ring of integers <math>\Z</math> is the field of [[rational number]]s <math>\Q.</math> The field of fractions of a field is [[isomorphism|isomorphic]] to the field itself.