---
tag: 065CK367F9
kind: concept
name: Coprime ideals
aliases: [comaximal-ideals]
msc: [13A15]
sources:
  - url: https://en.wikipedia.org/wiki/Chinese_remainder_theorem
    locator: Generalization to arbitrary rings
---

## Summary

Two ideals of a ring are coprime when their sum is the whole ring.
For the integers, the ideals $(m)$ and $(n)$ are coprime exactly when $m$ and $n$ are coprime numbers.
The [[definition of coprime ideals|0MDJP82TEH]] gives the condition.