Ring Theory Q: Show Idempotence in R/(f-f^2*g) with Example

[regularngon]

Homework Statement

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.

Homework Equations

None.

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]

Homework Statement

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.

Homework Equations

None.

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.

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