integers.

Then the field of fractions is the set with addition given by
: and multiplication given by
:One may check that these operations are well-defined and that, for any integral domain , is indeed a field. In particular, for , the multiplicative inverse of is as expected: .

The embedding of in maps each in to the fraction for any nonzero (the equivalence class is independent of the choice ). This is modeled on the identity .

The field of fractions of is characterized by the following

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