Division ring: Difference between revisions
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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 09:12, 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.