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Search: id:A127708
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| A127708 |
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Number of non-commutative rings with 1 containing n elements. |
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+0
2
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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
(list; graph; listen)
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OFFSET
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1,16
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COMMENT
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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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C. Noebauer, Home page.
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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 this_sequence A094896 A067155 A073867
Adjacent sequences: A127705 A127706 A127707 this_sequence 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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