---
tag: 0EA5BTA0CX
kind: concept
name: Division ring
aliases: [skew-field]
msc: ["12E15"]
sources:
  - url: https://en.wikipedia.org/wiki/Division_ring
    locator: lead section
same_as:
  wikidata: Q650741
  wikipedia: Division ring
---

## Summary

A division ring is a nonzero ring in which every nonzero element has a multiplicative inverse.
It is like a field, but the multiplication need not be commutative.
The [[definition of a division ring|0WZXK05ME7]] gives the conditions.