Ideal and factor ring

Question

I want to determine the ideals and factor rings for $R\times\mathbb{Z}_{116}$ and $Q \times\mathbb{Z}_9$

I know that $Q$ and $R$ are fields and their ideals are ${0}$ and $Q / R$ and the ideals in $\mathbb{Z}_n$ are $\{d\ast\mathbb{Z}_n : d \mid n\}$

I don't know how to work out the result.

Answer 1

You have everything you need. Keep in mind that $$ A\times B\unlhd C\times D\iff A\unlhd C\wedge B\unlhd D $$