---
tag: 096Z9MP2ME
kind: concept
name: Ideal
msc: [13A15]
sources:
  - url: https://en.wikipedia.org/wiki/Ideal_(ring_theory)
    locator: lead section
same_as:
  wikidata: Q44649
  wikipedia: Ideal (ring theory)
---

## Summary

An ideal of a ring is an additive subgroup that is closed under multiplication by every element of the ring.
Ideals are the kernels of ring homomorphisms, and they give quotient rings.
The [[definition of an ideal|0MYSA6MYNA]] gives the conditions.