# Difference between revisions of "Division ring"

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− | In [[algebra]], a '''division ring''' is a ring in which every non-zero element is invertible. | + | In [[algebra]], a '''division ring''' or '''skew field''' is a ring in which every non-zero element is invertible. |

A [[commutativity|commutative]] division ring is a [[field (mathematics)|field]]. | A [[commutativity|commutative]] division ring is a [[field (mathematics)|field]]. |

## Revision as of 14:12, 22 December 2008

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.