# Tagged Questions

A magma is a set together with a binary operation on this set. (For questions about the computer algebra system named Magma, use the [magma-cas] tag instead.)

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### Find the number of different magmas that have $A$ as its underlying set

I have a problem involving algebraic structures. Any help I can get here would be amazing. Problem: We have a set $A$, $\text{card} A = n$, $n \in \Bbb N$. Find the number of different magmas that ...
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### Ring like structure with non-associative “addition”

Is there any formally defined algebraic structure which consists of a set and two binary operations, where one is a commutative magma ("addition"), and the other is a semigroup ("multiplication"), (...
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### Are there useful visual representations of magmas?

In group theory we have Cayley graphs. Are there analogous or anyway useful visual representations of magma structures? I am unsure about how to construct a graph representing, for instance, a free ...
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### Cantor-Bernstein theorem for magmas

Let $G$, $H$ be magmas. $G_1 \subset G$ - submagma of $G$, $H_1 \subset H$ - submagma of $H$. Let $G \simeq H_1$, $H \simeq G_1$. Is true that $G \simeq H$?
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### Is this a free magma?

Given a context-free grammar $S\to(),S\to(SS)$, which generates all sentences of matching brackets in expressions of binary (possibly non associative) operations, and let $P$ be the set of all these ...
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### Is there a name for this property?

Is there a general name for the following properties, (similar to the properties of existence of an additive identity, existence of multiplicative identity etc): For any given set, the intersection ...
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### Normal Submagma?

Is there a definition of normal submagma? visit https://en.wikipedia.org/wiki/Magma_(algebra) For normal sub-quasi-group I found two: A sub-quasi-group $H$ is called normal if there exists a normal ...
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### Finding a binary operation on $\{1, \dots, n\}$ so that each $k$ has exactly $k - 1$ left inverses

What is an example of a binary operation on the set $\{1, \dots, n\}$ so that each element $k \in \{1, \dots, n\}$ has respectively $k-1$ left inverses? I have been trying various combinations with ...
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### Does the following property of the composition of a magma have a name?

If $M$ is a magma and $$+:M\times M\to M$$ is its law of composition, does the property $$(x+y)+z=x+(y+z)\qquad\forall\ x,y,z\in M :\quad y\neq x,z$$ have a name? It resembles the associativity of ...
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### Does this notion of “weak” isomorphism exist in literature?

Let $(M,\circ)$ and $(N,\ast)$ be two magmas. I'd like to relax the notion of isomorphism by defining a notion of "weak" isomorphism in the following way: $M$ and $N$ are "weakly" isomorphic if there ...
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### Associativity in category theory [closed]

In Category Theory, the composition of morphisms must be associative. What would happen if we give up this associative law? For example Lie algebras are vector spaces with non-associative binary ...
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### Referencing the construction of a left loop

We call left loop a magma $(L,\cdot)$ such that for all $(a,b)\in L\times L$, exists only one $x\in L$ such that $a\cdot x=b$, exists one $e\in L$ such that $e\cdot x=x=x\cdot e$ for all $x\in L$. ...
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### Isomorphism between two magmas with one.

Do we have a method to find one (or all) isomorphism between two given magmas with one using GAP? Edit If we have Loop or Latin square (with one) instead of Magma then do we have the method?
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### Proper term for a monotonic magma

Let $M$ be the multiplication table for a finite magma. Entries are labeled $0,\ldots,n-1$. M has the property that $M(i,j)\ge i, M(i,j) \ge j$. What is the proper term for this kind of magma and ...
I was playing around with the following object: Let $Q$ be a set with a binary operator $\cdot$ obeying the axioms: $a \cdot a = a$ (idempotence) $a \cdot (b \cdot c) = (a \cdot b) \cdot (a \cdot c)$...
I have a semigroup $S$ including a generator, say $d$, such that $$d^4=d$$ I am trying to guess the general rule of $d$'s powers such that when I want to calculate $d^n, n\in\mathbb N$; I can simplify ...