# Definition:Skew Field

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## Contents

## 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.

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 23$