login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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; 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..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 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 A200065 A067155

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 24 10:19 EST 2014. Contains 249882 sequences.