Editing Division ring (section)

== Related notions ==
Division rings ''used to be'' called "fields" in an older usage. In many languages, a word meaning "body" is used for division rings, in some languages designating either commutative or noncommutative division rings, while in others specifically designating commutative division rings (what we now call fields in English).  A more complete comparison is found in the article on [[Field (mathematics)|fields]].

The name "skew field" has an interesting [[lexical semantics|semantic]] feature: a modifier (here "skew") ''widens'' the scope of the base term (here "field"). Thus a field is a particular type of skew field, and not all skew fields are fields.

While division rings and algebras as discussed here are assumed to have associative multiplication, [[Division algebra#Not necessarily associative division algebras|nonassociative division algebras]] such as the [[octonion]]s are also of interest.

A [[near-field (mathematics)|near-field]] is an algebraic structure similar to a division ring, except that it has only one of the two [[distributive law]]s.