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:
“Becoming responsible adults is no longer a matter of whether children hang up their pajamas or put dirty towels in the hamper, but whether they care about themselves and others—and whether they see everyday chores as related to how we treat this planet.”
—Eda Le Shan (20th century)
“Hang ideas! They are tramps, vagabonds, knocking at the back- door of your mind, each taking a little of your substance, each carrying away some crumb of that belief in a few simple notions you must cling to if you want to live decently and would like to die easy!”
—Joseph Conrad (1857–1924)