28
votes
What's the maximum probability of associativity for triples in a nonassociative loop?
I found the following example due to J. Jezek and T. Kepka from "Notes on the number of associative triples" Acta Universitatis Carolinae 31 (1990), 15-19 (Example 2.1):
Suppose $Q(+)$ is ...
- 85.6k
5
votes
What's the maximum probability of associativity for triples in a nonassociative loop?
This is a bit too long for a comment, so it's an answer. The Loops package for Gap, by Gabor Nagy and Petr Vojtechovsky contains implementations of all the nonassociative Moufang loops of order $\leq ...
- 3,768
4
votes
What is the origin of the term magma?
Wikipedia also says that "magma" is used by Serre in his book Lie algebras and lie groups: 1964 Lectures given at Harvard University. This seems to be the case (at least for the 1992 Springer reprint ...
- 27.2k
2
votes
Accepted
Principal ideal of a non-associative magma
In a magma $M$, one can describe the 2-sided ideal generated by a subset $Y$ as follows: define by induction
$$M_1=M,\;Y_1=Y,\; M_n=\bigcup_{p,q\ge 1,p+q=n}M_pM_q,\;Y_n=\bigcup_{p,q\ge 1,p+q=n}(M_pY_q\...
- 63.9k
2
votes
Algebras determined by their globals
For which other classes of algebras (esp groupoids) is the result true?
One class of groupoids with this property is the class of
groups considered as groupoids.
That is, if ${\mathcal U}(G,\ast)\cong{...
- 14.6k
1
vote
On the notion of partial semigroup
I realize that this is a question is nearly a decade old, but hopefully someone will find this helpful. One thing that is notable about using (4) as our definition for a partial semigroup is that it ...
- 305
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