---
tag: 0CD87SFM2N
kind: concept
name: Two-sided ideal
msc: [16D25]
sources:
  - url: https://en.wikipedia.org/wiki/Ideal_(ring_theory)
    locator: Definitions
---

## Summary

A two-sided ideal of a ring is an additive subgroup that is closed under multiplication by ring elements on the left and on the right.
The two-sided ideals are the kernels of ring homomorphisms.
The [[definition of a two-sided ideal|0DDA6CY7GJ]] gives the conditions.