Let $A$ be a commutative algebra with unit. Let $A[x]$ be the polynomial algebra with coefficients in $A$ with the standard gradation (by degrees).
I have the following questions.
What are maximal homogeneous ideal in $A[x]$ not containing $A[x]_{+}:=\bigoplus\limits_{n>0}Ax^n$? How can I describe them in terms of maximal ideals in $A$?
My idea is something like:
If $I \subset A$ maximal ideal, then $\bigoplus\limits_{n\geq0}Ix^n$ is a maximal ideal among them that not contain $A[x]_+$. But it looks like miss something.