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%I A127708
%S A127708 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
%N A127708 Number of non-commutative rings with 1 containing n elements.
%C A127708 We consider rings in which multiplication is associative and has a unit, 
               but where there is at least one pair of non-commuting elements.
%H A127708 C. Noebauer, <a href="http://www.algebra.uni-linz.ac.at/~noebsi/">Home 
               page</a>.
%e A127708 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.
%Y A127708 Cf. A037291, A127707.
%Y A127708 Sequence in context: A144546 A165970 A081357 this_sequence A094896 A067155 
               A073867
%Y A127708 Adjacent sequences: A127705 A127706 A127707 this_sequence A127709 A127710 
               A127711
%K A127708 more,nice,nonn
%O A127708 1,16
%A A127708 Hugues Randriam (randriam(AT)enst.fr), Jan 24 2007, Jan 29 2007

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