# Questions tagged [magma]

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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### Group sufficiency conditions given an associative magma. [duplicate]

From Bourbaki's Algebra. I desire to see how others think about these interesting questions involving surjectivity and injectivity of translations. (4.2) This problem is marked as difficult. Problem a:...
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### Given that $f$ and $g$ are homomorphisms, the implication that $f \odot g$ is also a homomorphism implies $(S, \odot)$ is entropic - why?

Context: Seth Warner's "Modern Algebra" (1965), exercise $13.13$. Ongoing self-study. Let $(S, \odot)$ and $(T, \otimes)$ be closed algebraic structures with one operation. Let $(S, \odot)$ ...
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### Is there a magma with the following property?

Does there exist an infinite magma with the following property: Let $n$ be a positive integer greater than or equal to $2$. For all $x_1,...,x_n$, if $x_1,...x_n$ are all distinct, then all products ...
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### What is the formal definition of a Cayley table?

What is the formal definition of a Cayley table? I am not interested merely in Cayley tables for groups, I am interested in general Cayley tables for non-empty finite magmas. Also, another question is,...
1 vote
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### Term for a semigroup with left identities and left inverses?

Is there a term for a semigroup $(M, *)$ that has at least one left identity and left inverses in the "weak" sense that, for all $a \in M$, there exists a $b \in M$ such that $b*a$ is a left ...
1 vote