Ring

Division ring

A division ring¹² is a ring in which every nonzero element is a multiplicative unit. Every such ring is simple. See also Division algebra.

Properties

• Wedderburn’s little theorem states every finite division ring is a field.

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Footnotes

1. German Divisionsring. ↩

2. 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. ↩