# Math Help - ideal and quotient ring

1. ## ideal and quotient ring

hi, i'm having trouble doing this question. I'm not sure how to start it.
Any help?

Thanks

2. Originally Posted by gkz
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 $\alpha=x+$. Then, an elements of R[x]/<x^2+1> has the form $k_1 + k_2\alpha$, where k_1, k_2 $\in$ R. I leave it to you to fill the remaining steps.