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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 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: A165970 A285180 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

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Last modified July 23 04:04 EDT 2017. Contains 289686 sequences.