hi, i'm having trouble doing this question. I'm not sure how to start it.
Any help?
Thanks
Hint) Verify that I is an ideal, written <x^2 +1>. Since x^2 + 1 is irreducible in R=R[x] and R is PID, <x^2 +1> is a maximal ideal in R It follows that R[x]/<x^2+1> is a field. Let $\displaystyle \alpha=x+<x^2+1>$. Then, an elements of R[x]/<x^2+1> has the form $\displaystyle k_1 + k_2\alpha$, where k_1, k_2 $\displaystyle \in$ R. I leave it to you to fill the remaining steps.