Division ring

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. 

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