This problem is from Dummit and Foote Abstract Algebra
Exhibit all of the ideals in the ring
, where F is a field and is a polynomial in (describe them in terms of the factorization of p(x)))
I know that since F is a field that is a PID and a UFD.
So since and where each is irreduceable and this is unique upto associates. Also since each the Ideal of
First I am not sure if the above observations help me, If they do I don't see where to go from here. Second I am having a hard time visualzing what elements of this ring would look like. I think it would eliminate all elements of F[x] that have the same degree as any factor of .