# 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.

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### How can I build free unital magmas?

N. Bourbaki formally defines the free magma $M(X)$ over a set $X$. However, it does not define the free unital magma over $X$, which I am denoting by $M^{\ast}(X)$ (maybe you know some more common ...
1 vote
186 views

### Example of idempotent left quasigroups which are right-distributive but not left-distributive

I am looking for examples of the following algebraic structure: a set (X,.) which satisfy the axioms (idempotent) x.x = x (left quasigroup) the equation a.x = b has a unique solution denoted by x = ...
97 views

### A multiplication for distributive lattices via rowmotion

Let $L$ be a finite distributive lattice. In case $L$ is Boolean one can define a multiplication by $a*b:=(a \cup b) \setminus (a \cap b)=(a \cup b) \cap (a \cap b)^c$, where $(-)^c$ denotes the ...
120 views

### Principal ideal of a non-associative magma

The definitions of an ideal of an algebraic structure $A$ (as a substructure $I$ such that the product of $A$ and $I$ is a subset of $I$) do not involve associativity. However, the definitions of a ...
651 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
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### 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(=...
333 views

### For a new operation on a finite group of odd order giving a loop structure, when does this also gives a group

For finite groups $G$ of odd order, as $x \mapsto x^2$ is bijection (but no automorphism in general) then, we can define for each $g \in G$ the element $x^{1/2}$ by requiring $(x^{1/2})^2 = x$. Then ...
107 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 ...
291 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 ...
848 views

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### 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?