# Definition:Skew Field

## Definition

A skew field is a division ring whose ring product is specifically not commutative.

## Also known as

The term sfield is sometimes encountered.

Some sources do not bother to give a specific name to this concept, but merely refer to a non-commutative division ring.

## Examples

### Quaternions form Skew Field

The set $\H$ of quaternions forms a skew field under the operations of addition and multiplication.

## Also see

• Results about skew fields can be found here.