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

.

Thanks

TES