1. The problem statement, all variables and given/known data Let R be a commutative ring and a,b in R. Show that the canonical image of ab in R/(f - f^2*g) is idempotent. Give an example where this idempotent is not 0 or 1. 2. Relevant equations None. 3. The attempt at a solution Well I've tried playing with the properties of ideals such as multiplicative closure under R but I've had no luck.