Every Ideal of the Direct Product of Rings is the Direct Product of Ideals
Problem 536
Let $R$ and $S$ be rings with $1\neq 0$.
Prove that every ideal of the direct product $R\times S$ is of the form $I\times J$, where $I$ is an ideal of $R$, and $J$ is an ideal of $S$.
Add to solve later 
