|
| |
|
|
A127708
|
|
Number of non-commutative rings with 1 containing n elements.
|
|
1
| |
|
|
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,16
|
|
|
COMMENTS
| We consider rings in which multiplication is associative and has a unit, but where there is at least one pair of non-commuting elements.
|
|
|
LINKS
| C. Noebauer, Home page [broken link].
|
|
|
EXAMPLE
| a(n)=0 for n<=7 and a(8)=1, so all rings (with unit) of cardinality at most 7 are commutative, while the smallest non-commutative ring (with unit) has cardinality 8 and is unique up to isomorphism; it can be represented as the ring of upper-triangular matrices of size 2 over F_2.
|
|
|
CROSSREFS
| Cf. A037291, A127707.
Sequence in context: A144546 A165970 A081357 * A094896 A067155 A073867
Adjacent sequences: A127705 A127706 A127707 * A127709 A127710 A127711
|
|
|
KEYWORD
| more,nice,nonn
|
|
|
AUTHOR
| Hugues Randriam (randriam(AT)enst.fr), Jan 24 2007, Jan 29 2007
|
| |
|
|
