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A127708
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Number of non-commutative rings with 1 containing n elements.
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1
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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
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OFFSET
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1,16
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COMMENTS
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We consider rings in which multiplication is associative and has a unit, but where there is at least one pair of non-commuting elements.
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LINKS
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Table of n, a(n) for n=1..31.
C. Noebauer, Home page [broken link].
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EXAMPLE
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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.
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CROSSREFS
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Cf. A037291, A127707.
Sequence in context: A144546 A165970 A081357 * A094896 A200065 A067155
Adjacent sequences: A127705 A127706 A127707 * A127709 A127710 A127711
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KEYWORD
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more,nice,nonn
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AUTHOR
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Hugues Randriam (randriam(AT)enst.fr), Jan 24 2007, Jan 29 2007
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STATUS
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approved
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