PlanetMath: division ring

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division ring

(Definition)

A division ring is a ring $D$ with identity such that

$1 \neq 0$
For all nonzero $a \in D$ there exists $b \in D$ with $a \cdot b = b \cdot a = 1$

Every field is a commutative division ring. The Hamiltonian quaternions are an example of a division ring which is not a field.

"division ring" is owned by djao.

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Other names:

skew field

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Cross-references: Hamiltonian quaternions, commutative, field, identity, ring
There are 51 references to this entry.

This is version 5 of division ring, born on 2001-10-19, modified 2006-10-22.
Object id is 356, canonical name is DivisionRing.
Accessed 10935 times total.

Classification:

16K99 (Associative rings and algebras :: Division rings and semisimple Artin rings :: Miscellaneous)

Pending Errata and Addenda

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