The ring of fractions of an integral domain. The field of fractions of the ring of integers Z is the rational field Q, and the field of fractions of the polynomial ring K[X_1, X_2, ..., X_n] over a field K 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)) : auto right match f, g element K[X_1, X_2, ..., X_n], g!=0}. The field of fractions of an integral domain R is the smallest field containing R, since it is obtained from R by adding the least needed to make R a field, namely the possibility of dividing by any nonzero element.

localization | ring of fractions | total ring of fractions