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 non-commutative 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 Field (mathematics).
Skew fields have an interesting 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, nonassociative division algebras such as the octonions are also of interest.
A near-field is an algebraic structure similar to a division ring, except that it has only one of the two distributive laws.
Read more about this topic: Division Ring
Famous quotes containing the words related and/or notions:
“Gambling is closely related to theft, and lewdness to murder.”
—Chinese proverb.
“The mass believes that it has the right to impose and to give force of law to notions born in the café.”
—José Ortega Y Gasset (1883–1955)