|
| |
|
|
A127708
|
|
Number of non-commutative rings with 1 containing n elements.
|
|
11
|
|
|
|
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, 99, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0
(list;
graph;
refs;
listen;
history;
text;
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
|
Table of n, a(n) for n=1..63.
C. Noebauer, Home page [Archived copy as of 2008 from web.archive.org]
|
|
|
FORMULA
|
a(n) = A037291(n) - A127707(n). - Bernard Schott, Apr 19 2022
|
|
|
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.
A037291(32) = 208, A127707(32) = 109, hence a(32) = 208 - 109 = 99.
|
|
|
CROSSREFS
|
Cf. A027623, A037291, A127707, A209401, A342376.
Sequence in context: A165970 A285180 A081357 * A094896 A277118 A200065
Adjacent sequences: A127705 A127706 A127707 * A127709 A127710 A127711
|
|
|
KEYWORD
|
nonn,nice,more
|
|
|
AUTHOR
|
Hugues Randriam (randriam(AT)enst.fr), Jan 24 2007, Jan 29 2007
|
|
|
EXTENSIONS
|
a(32)-a(63) from Bernard Schott, Apr 19 2022
a(54) corrected by Andrey Zabolotskiy, Feb 02 2023
|
|
|
STATUS
|
approved
|
| |
|
|
