Let $R$ be a ring.

Two ideals $I$ and $J$ of $R$ are said to be comaximal if $I + J = R$ If $R$ is unital, this is equivalent to requiring that there be $x\in I$ and $y\in J$ such that $x+y=1$

For example, any two distinct maximal ideals of $R$ are comaximal.

A set $\cal S$ of ideals of $R$ is said to be pairwise comaximal (or just comaximal) if $I+J=R$ for all distinct $I,J\in\cal S$