Article View: aus.mathematics
Article #171Re: Name of an operator-set combination
From: Ken Pledger
Date: Tue, 12 Dec 2006 21:10
Date: Tue, 12 Dec 2006 21:10
30 lines
2576 bytes
2576 bytes
In article <ek5n0n$cai$1@news-01.bur.connect.com.au>,
"Diamond, Mark" <dot@dot.dot> wrote:
> Could someone please tell me if the operator-set combination, where the
> operator is commutative but NOT associative, has any special name. For
> example, (fixed font makes this look correct) ...
>
> . | 0 | 1 | 2 | 3 |
> -------------------
> 0 | 0 3 2 1
> 1 | 3 1 0 2
> 2 | 2 0 1 3
> 3 | 1 2 3 0
>
> If it does, I'd very much like to know what it is.
>
> Cheers,
>
> Mark Diamond
It's just a commutative groupoid, although your particular example
happens to be a commutative quasigroup. (In a quasigroup the equation
xy = z determines each of x, y, z uniquely from the other two.)
I'm sorry this reply is so late. If you'd like to post to news
groups carrying more traffic than <aus.mathematics>, you might like to
try <sci.math> or <alt.math.undergrad>.
Ken Pledger.
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