# Maximal Ideals in $K[y]$

Let $K=F[x]/(p(x))$, where $F$ is a field, $p(x)\in F[x]$ is an irreducible polynomial.

What are all the maximal ideals in $K[y]$?

Attempt: I have an attempt, but not entirely sure it is correct.

Since $(p(x))$ is a maximal ideal in $F[x]$, this means $K$ is actually a field.

Thus $K[y]$ is a PID.

So maximal ideals in $K[y]$ are $(g(y))$ for irreducible polynomials $g(y)\in K[y]$?

• That's correct. – Bernard Aug 22 '16 at 9:51