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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

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 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

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

License Agreements, Terms of Use, Privacy Policy .

Last modified December 9 17:46 EST 2016. Contains 278985 sequences.