Would appreciate so much if anyone could show me how to this questions (exam tomorrow ah!)
Consider the ring R=Z[X] and let
I={f(X) in R : f(X)= 9g(X)+(X^2 -1)h(X) for some g(X),h(X) in R}
be the ideal of R generated by the elements 9 and X^2 -1
a. find all the ideals of R which contain I
b. For every maximum ideal J of R containing I, use the fundamental isomorphism theorem for rings to prove the quotient ring R/J is isomorphic to Z3 (3 is a lower subscript)
Thank you!