---
tag: 0076HWHGHQ
kind: concept
name: Quotient ring
aliases: [factor-ring]
msc: [16D25]
sources:
  - url: https://en.wikipedia.org/wiki/Quotient_ring
    locator: lead section
same_as:
  wikidata: Q619436
  wikipedia: Quotient ring
---

## Summary

The quotient ring of a ring by a two-sided ideal is the set of the cosets of the ideal.
Its operations come from the operations of the ring.
The integers modulo $n$ are the main example.
The [[definition of the quotient ring|0VFW4Y69BT]] gives the construction.