# Homework Help: Correspondence theorem for rings

1. Jan 30, 2012

### sleventh

Hello,

"What does the correspondence theorem tell us about ideals in Z[x] that contain x$^{2}$ + 1?

My thinking is that since Z[x]/(x$^{2}$ + 1) is surjective map and its kernel is principle and generated by x$^{2}$ + 1 since x$^{2}$ + 1 is irreducible. This implies ideals that contain x$^{2}$ + 1 are principle and isomorphic to C.

I'm not sure if (a) my reasoning is right and (b) what answer this question is trying to get from us.