Let $K$ be a field, let $R=K[x]$, and let $A\ne 0 \in R$. If $m > \deg(A) $, it is to show that there are no ideals $I_{1}=AR, I_{2},\ldots,I_{m}$ of $R$, all different from each other, such that $I_{1} \subset I_{2} \subset \cdots\subset I_{m}$.
This exercise is from a algebra book and I want to do it, but I don't see how to begin.
Does anybody see the beginning?
Tell me . Please.