A027623 (rings with n elements)

Edwin Clark eclark at math.usf.edu
Sat Aug 16 04:33:38 CEST 2003


This was given as an illustration in Neil's Notices article. I took a look
at it:

The offset is given as 0: 

But if (R,+,*) is a ring then (R,+) is an abelian group
and so must contain an additive identity. So R has at least one element
and there is no ring with 0 elements, n'est pas? 

I notice that the definition given of a group doesn't include a 0, but I
haven't heard of that definition of a group. Also sequence  A000688 which
gives the number of abelian groups has offset = 1.  

It should be changed to begin with 0 or the offset changed to 1, IMHO.

--Edwin






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