Definition:Magma/Also known as
Magma: Also known as
The word magma is a recently-coined term, and as such has not yet fully filtered into the mainstream literature.
Thus a magma is frequently referred to by description, as a closed algebraic structure.
Another 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).
Some sources use the term monoid, in particular when its operation is commutative, but this is not endorsed on $\mathsf{Pr} \infty \mathsf{fWiki}$, as monoid is used for something else.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): monoid: 2.
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 4.4$. Gruppoids, semigroups and groups
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 5$: Groups $\text{I}$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): groupoid
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): groupoid