Determine all the ideals of $\mathbb{Z}_7 \times \mathbb{Q}$
The short but annoying question to think. The answer is $\{0,0\}$ and itself (such a trivial problem) which I found in the manual solution section (and it doesn't show its steps or some explanations) , I really don't know how to get it. I have read my textbook but found no information. Please, help.
The ideals of $R\times S$ are exactly of the form $I\times J$ where $I\lhd R$ and $J\lhd S$.
The assertion you gave about there being only two ideals is wrong.