# 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 $\mathcal{S}$ of ideals of $R$ is said to be *pairwise comaximal* (or just *comaximal*) if $I+J=R$ for all distinct $I,J\in \mathcal{S}$.

Title | comaximal ideals |
---|---|

Canonical name | ComaximalIdeals |

Date of creation | 2013-03-22 12:35:57 |

Last modified on | 2013-03-22 12:35:57 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 8 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 16D25 |

Related topic | MaximalIdeal |

Defines | comaximal |