Definition:Magma
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Definition
A magma is an algebraic structure $\left({S, \circ}\right)$ which is closed.
Note that as usually defined, $\varnothing \subseteq S$, that is, the underlying set is allowed (in the extreme case) to be the empty set.
However, some treatments insist that $S \ne \varnothing$.
Linguistic note
The term magma was coined by the Bourbaki group. The word has several meanings in French, but its interpretation as jumble is the one which was probably originally intended.
Also known as
An older term for this concept is groupoid (or gruppoid). This word was first coined by Øystein Ore.
The term groupoid is often used for a completely different concept in category theory.
The word groupoid arises as a back-formation from group in the same way as humanoid derives from human.
The word gruppoid (rarely found in English) is the German term (from the German gruppe for group).
Also see
- Results about magmas can be found here.
Sources
- J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 4.4$
