# 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 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 $I,J\in\cal S$.

Title comaximal ideals ComaximalIdeals 2013-03-22 12:35:57 2013-03-22 12:35:57 yark (2760) yark (2760) 8 yark (2760) Definition msc 16D25 MaximalIdeal comaximal