Division ring: Difference between revisions
Jump to navigation
Jump to search
imported>Richard Pinch m (link) |
mNo edit summary |
||
| (2 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
{{subpages}} | |||
In [[algebra]], a '''division ring''' or '''skew field''' is a [[ring (mathematics)|ring]] in which every non-zero element is invertible. | In [[algebra]], a '''division ring''' or '''skew field''' is a [[ring (mathematics)|ring]] in which every non-zero element is invertible. | ||
| Line 9: | Line 10: | ||
==References== | ==References== | ||
* {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55540-9 | pages=84,642 }} | * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55540-9 | pages=84,642 }}[[Category:Suggestion Bot Tag]] | ||
Latest revision as of 16:01, 7 August 2024
In algebra, a division ring or skew field is a ring in which every non-zero element is invertible.
A commutative division ring is a field.
The centre C of a division ring A is a field, and hence A may be regarded as a C-algebra.
Examples
- The quaternions form a division ring.
References
- Serge Lang (1993). Algebra, 3rd ed. Addison-Wesley, 84,642. ISBN 0-201-55540-9.