 For an example of a projective limit, see .The localization generalizes the construction of the field of fractions of an integral domain to an arbitrary ring and modules.Given a (not necessarily commutative) ring "R" and a subset "S" of "R", there exists a ring formula_174 together with the ring homomorphism formula_175 that "inverts" "S"; that is, the homomorphism maps elements in "S" to unit elements in formula_176, and, moreover, any ring homomorphism from "R" that "inverts" "S" uniquely factors through formula_176.