A a UFD, S⊆A a saturated multiplicative subset not containing 0. Then S-1A is a UFD.

Lemma 1. S contains all the units in A.
Lemma 2. In general, if an element of a ring is irreducible then so are its associates.
Proposition 3. If a∈A\S is irreducible in A then it is irreducible in S^-1A.
Lemma 4. a∈A is a unit in S^-1A if and only if a∈S.
Proposition 5. If a is irreducible in S^-1A then it is nonzero, nonunit in A, and its factorization is of the form a=s₁s₂…s_rb, b∉S.
Proposition 6.S^-1A is a UFD.