Originally Posted by
Ryaη Is it anything like this?
For some ring R that has A and B as ideals.
$\displaystyle nA \in R$ and $\displaystyle nB \in R$, then $\displaystyle nA+nB \in R$. Thus, $\displaystyle n(A+B) \in R$. Therefore $\displaystyle (A+B) \in R$.