Sum of ideals ($I+J$)

The sum of two ideals $I,J$ of a ring isIt 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 $b\in J$.