The extension ring obtained from a commutative unit ring (other than the trivial ring) when allowing division by all non-zero divisors. The ring of fractions of an integral domain is always a field. The term "ring of fractions" is sometimes used to denote any localization of a ring. The ring of fractions in the above meaning is then referred to as the total ring of fractions, and coincides with the localization with respect to the set of all non-zero divisors.

field of fractions | fraction | localization | ring | total ring of fractions