Hi. New to the board. I need some help figuring out the following answer.

For each of the rings Z(60) and F[x]/[(x^4)+(2x^3)+(x^2)], find all their ideals and identify all their homomorphic images.

For example, 5 in Z(60) creates a principal ideal (5) and [Z(60)]/(5) is isomorphic with Z(5).

Hint: Use the surjective homomorphism Z to Z(60) to show that ideals of Z(60) correspond to ideals of Z containing the ideal (60), and so on.

Really lost. Thanks.