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.

#state/tidy | #lang/en | #SemBr

German Divisionsring. ↩
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. ↩