| 21. | It holds in a projective plane over any field, but fails for projective planes over any noncommutative division ring.
|
| 22. | Lastly, there is even an example of a domain in a division ring which satisfies " neither"
|
| 23. | According to Wedderburn's little theorem, any finite division ring must be commutative, and hence a finite field.
|
| 24. | From the bundle theorem follows the existence of a ) a skewfield ( division ring ) and b ) an ovoid.
|
| 25. | The Artin Wedderburn theorem reduces classifying simple rings over a division ring to classifying division rings that contain a given division ring.
|
| 26. | The Artin Wedderburn theorem reduces classifying simple rings over a division ring to classifying division rings that contain a given division ring.
|
| 27. | The Artin Wedderburn theorem reduces classifying simple rings over a division ring to classifying division rings that contain a given division ring.
|
| 28. | Beginning with division rings arising from geometry, the study of noncommutative rings has grown into a major area of modern algebra.
|
| 29. | Division rings can be roughly classified according to whether or not they are finite-dimensional or infinite-dimensional over their centers.
|
| 30. | Failure of one of the two distributive laws brings about near-rings and near-fields instead of rings and division rings respectively.
|
