

A127708


Number of noncommutative 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;
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 noncommuting elements.


LINKS

Table of n, a(n) for n=1..31.
C. Noebauer, Home page [Archived copy as of 2008 from web.archive.org]


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 noncommutative ring (with unit) has cardinality 8 and is unique up to isomorphism; it can be represented as the ring of uppertriangular matrices of size 2 over F_2.


CROSSREFS

Cf. A037291, A127707.
Sequence in context: A144546 A165970 A081357 * A094896 A277118 A200065
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


STATUS

approved



