The ring of fractions of an integral domain. The field of fractions of the ring of integers 
is the rational field 
, and the field of fractions of the polynomial
ring ![K[X_1,X_2,...,X_n]](/images/equations/FieldofFractions/Inline3.svg)
over a field 
is the field of rational functions
![K(X_1,X_2,...,X_n)={(f(X_1,X_2,...,X_n))/(g(X_1,X_2,...,X_n)):
f,g in K[X_1,X_2,...,X_n],g!=0}.](/images/equations/FieldofFractions/NumberedEquation1.svg) |
The field of fractions of an integral domain 
is the smallest field containing 
, since it is obtained from 
by adding the least needed to make 
a field, namely the possibility of dividing by any nonzero
element.
