Ring theory question

regularngon

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.

matt grime

Surely this will depend on the relationship between a,b and f,g.

HallsofIvy

Please explain what you are talking about! What are f and g? Are they members of R?