Sum of ideals
= Sum of ideals
{title2=$I+J$}
The sum of two <ideals> $I,J$ of a <ring> is
$$
I+J=\{a+b:a\in I,\ b\in J\}.
$$
It is the smallest <ideal> containing both $I$ and $J$: it is closed under subtraction and multiplication by ring elements, and any <ideal> containing $I$ and $J$ contains every such sum. The <ideals> are <comaximal ideals> when $I+J=R$, equivalently when $1=a+b$ for some $a\in I$ and $b\in J$.