# 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.

**0**

votes

**0**answers

99 views

### A magma with the property (xy)(zt) = x(yz)t

Let $(M,\cdot)$ be a magma. Does the property $(x\cdot y)\cdot(z\cdot t) = x\cdot(y\cdot z)\cdot t$ have a special name? Thanks.

**17**

votes

**2**answers

431 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

**0**answers

55 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

**0**answers

93 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

**1**answer

267 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

**4**answers

637 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,...

**10**

votes

**2**answers

894 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

**1**answer

594 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

**2**answers

935 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 ...