Let R R be an associative ring with 1 1 , and Q Q its maximal ring of right quotients. If r r belongs to R R , a right insulator for r r in R R is a finite subset of R , { r i } i = 1 m R,\{ {r_i}\} _{i = 1}^m , such that the right annihilator of { r r i ; i = 1 , … , m } \{ r{r_i};i = 1, \ldots ,m\} is zero. Then we have: If Q Q is a projective right R R -module, Q Q is finitely generated; if R R is nonsingular, then Q Q is projective as a right R R -module if and only if there exists e = e 2 e = {e^2} in R R such that e R eR is injective and e e has a right insulator in R R ; under these circumstances, R = Q R = Q if and only if e e has a left insulator in R R . We prove some related results for torsionless Q Q , and give an example of a prime ring R R such that Q Q is a cyclic projective right R R -module, but R ≠ Q R \ne Q .