I have tried to solve an exercise regarding integral ring extensions which asked me to prove this:
If each of $\{R_i\mid i=1\ldots n\}$ is a family of integral ring extensions of a ring $R$, then $\prod_{i=1}^n R_i$ is an integral extension of $R$ as well.
It seems simple but I am not sure how I should prove that the polynomial is also monic