[[Ring]]
# Division ring

A **division ring**[^de][^alt] is a [[ring]] in which every nonzero element is a [[Unit|multiplicative unit]].
Every such ring is [[Simple ring|simple]].
See also [[Division algebra]].

[^de]: German _Divisionsring_.
[^alt]: Also called a **skew field** (German _Schiefkörper_). I prefer the term division ring because a division ring is a ring, but a skew field is not necessarily a field.

## Properties

- [[Wedderburn's little theorem]] states every finite division ring is a field.

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