conjecture: if p is prime, the no. of rings of order p^2 is 11

[Edwin Clark]

On Tue, 15 Apr 2008, Andrew Weimholt wrote:

> On 4/15/08, Christian G. Bower <bowerc at usa.net> wrote:
>>
>>
>> John Conway did a proof of a(p^2)=11 in that discussion from 1998. I can post
>> it if anyone is interested.
>>
>
> I'm interested :-)
>
> Andrew
>


MathSciNet has this:

MR1240670 (95f:16022)
Fine, Benjamin(1-FRF)
Classification of finite rings of order $p\sp 2$. (English summary)
Math. Mag. 66 (1993), no. 4, 248--252.
16P10
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The author calculates the eleven isomorphism classes of rings of order 
$p^2$, $p$ a prime, via generators and relations. This classification, in 
essence, dates back at least to G. Scorza [Rend. Accad. Sci. Fis. Mat. 
Napoli (3) 28 (1922), 65--79; Jbuch 48, 119] and R. Ballieu [Ann. Soc. 
Sci. Bruxelles Sér. I 61 (1947), 117--126; MR0020076 (8,499h)].