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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

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Last modified October 21 19:01 EDT 2014. Contains 248377 sequences.