| 1. | Every division ring is therefore a division algebra over its center.
|
| 2. | The only non-associative division algebra is the algebra of octonions.
|
| 3. | Because it is possible to divide quaternions, they form a division algebra.
|
| 4. | See for example normed division algebras and Banach algebras.
|
| 5. | The Brauer group arose out of attempts to classify division algebras over a field.
|
| 6. | If, then cannot be a division algebra.
|
| 7. | Associative division algebras have no zero divisors.
|
| 8. | :There are useful algebras that have neither a norm nor that are division algebras.
|
| 9. | Okubu's example was the algebra of 3 by 3 non-associative division algebra.
|
| 10. | Shafarevich stated his theorem for local fields in terms of division algebras rather than the fundamental class.
|
मोबाइल