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 $g(y)\in K[y]$?