Questions tagged [magmas]
Questions involving the algebraic structure called magma. Often used in combination with more general tags such as universal-algebra or the top-level tag ra.rings-and-algebras.
9
questions
24
votes
2answers
587 views
What's the maximum probability of associativity for triples in a nonassociative loop?
In a finite nonabelian group, the probability that two randomly chosen elements commute cannot exceed 5/8. One easy proof also makes it easy to find the smallest groups that attain this bound, namely ...
1
vote
0answers
60 views
Information on structure (CI-magma with (non surjective)homorphism) of chemical transformations
Thinking about the mathematical structure of chemical transformations, between all possible components (educts, products) it occurs to me, that this structure is a commutative-idempotent groupoid(=...
2
votes
0answers
97 views
Quasigroups extracted from the rational numbers and division
Consider a quasigroup $(Q,/)$, that is, Q is a set and for $\forall a,b\in Q$ there are unique solutions to the equations $x/a=b$ and $a/y=b$. How to find a maximal set of independent representants of ...
2
votes
1answer
274 views
Reference request for generalization of groups with out identity element?
In other words what do we call a magma which is associative and has divisibility property but not existence of identity? Or a groupoid when it loses the identity property?
A reference on such ...
4
votes
4answers
699 views
On the notion of partial semigroup
A partial binary operation on a set $X$ is just a (partial) function $\varphi: X \times X \rightharpoonup X$ (I'm using \rightharpoonup for partial maps), and a partial magma is a pair $\mathbb M = (M,...
30
votes
5answers
5k views
How many binary operations are associative?
Let $X$ be a finite set of $n$ elements, and consider a binary operation $\odot: X \times X \rightarrow X$. There are $n^{n^2}$ such binary operations, as the $n \times n$ table entries can each
be ...
10
votes
2answers
989 views
What is the origin of the term magma?
Wikipedia credits Bourbaki with coining it, but doesn't provide a source. Does anyone happen to know the motivation for using this term?
9
votes
1answer
638 views
Magma “actions” (or alternatively, “What is the Yoneda lemma for magmas?”)
Arguably the most import thing about groups, semigroups and more generally categories, is that they can act on sets (or even collections of sets in the case of a category). This is the basis for all ...
5
votes
2answers
994 views
Free commutative magma over a set
BOURBAKI, inside his book on ALGEBRA defines and provides explicit constructions concerning the concepts of free magma, free monoid (and implicitly free semi-group) and free group, and as well free ...
