# Division ring

From Citizendium

In algebra, a **division ring** or **skew field** is a ring in which every non-zero element is invertible.

A commutative division ring is a field.

The centre *C* of a division ring *A* is a field, and hence *A* may be regarded as a *C*-algebra.

## Examples

- The quaternions form a division ring.

## References

- Serge Lang (1993).
*Algebra*, 3rd ed. Addison-Wesley, 84,642. ISBN 0-201-55540-9.