---
tag: 0PV74TR5FP
kind: concept
name: Maximal ideal
msc: [13A15]
sources:
  - url: https://en.wikipedia.org/wiki/Maximal_ideal
    locator: lead section
same_as:
  wikidata: Q1203540
  wikipedia: Maximal ideal
---

## Summary

A maximal ideal of a ring is a proper ideal that is not contained in a larger proper ideal.
The maximal ideals of $\mathbb{Z}$ are the ideals $p\mathbb{Z}$ for $p$ prime.
The [[definition of a maximal ideal|09J6KGT65G]] gives the conditions.