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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Prove that this is a group

Let $G$ be a finite, nonempty set with an operation $*$ such that $G$ is closed under $*$ and $*$ is associative Given $a,b,c \in G$ with $a*b=a*c$, then $b=c$. Given $a,b,c \in G$ with $b*a=c*a$, ...
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Associativity for Magma

Say I have the operation table for a magma. I want to know whether or not the operation is associative. However, associativity is defined for an operation on 3 elements, and the operation table deals ...
3
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Properties of finite magmas $(S,\cdot)$ with $\forall(x,y,z)\in S^3, x\cdot(y\cdot z)=y\cdot(x\cdot z)$?

I am considering finite magmas $(S,\cdot)$ with $\forall(x,y,z)\in S^3, x\cdot(y\cdot z)=y\cdot(x\cdot z)$. Any finite commutative group is an example of such thing. But in the context (this question ...
3
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2answers
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Existence of an operation $\cdot$ such that $(a*(b*c))=(a\cdot b)*c$

When we can define a binary operation $\cdot:M\times M\rightarrow M$ on an algebraic structure $(M,*)$ such that $$a*(b*c)=(a\cdot b)*c$$ If $*$ is associative then $\cdot=*$ even if I'm not sure ...
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$\beta_a(n)=(a_1*\cdots(a_n*b))\setminus_* b$ and Iterations in right divisible magmas e representability by left translations.)

Let's consider the magma $(G,*)$ with infinite elements. Now I define $\operatorname{left}(G)$ the set of all the left translations $$\operatorname{left}(G):\{L_a:a \in G ,L_a(b)=a*b\}$$ And ...