comaximal ideals

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 (http://planetmath.org/Ring), this is equivalent to requiring thatthere 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 $𝒮$ of ideals of $R$ is said to be pairwise comaximal (or just comaximal) if $I+J=R$ for all distinct $I,J\in 𝒮$.