# Definition:Magma/Also known as

## Magma: Also known as

The word **magma** is a recently-coined term, and as such has not yet 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 $\text{I}$