---
type: "concept"
title: "Maximal ideal"
slug: "ideal-maximal"
language: "en"
translationGroupId: "cmrbt0hhq0001ls01cnlmqtv4"
domain: "Algebra"
status: "usable"
aliases: []
lastEditedBy: "ancient-tree"
---

An [[Ideal|ideal]] $M$ of a [[Commutative ring|commutative ring]] $A$ is maximal if $M\neq A$ (it is [[Proper subset|proper]]) and there is no ideal $I$ of $A$ such that
$$M \subsetneq I \subsetneq R.$$