Definition:Magma

Definition
A magma is an algebraic structure $\struct {S, \circ}$ such that $S$ is closed under $\circ$. That is, a magma is a pair $\struct {S, \circ}$ where:
 * $S$ is a set
 * $\circ : S \times S \to S$ is a binary operation on $S$

Also defined as
Note that as usually defined, $\O \subseteq S$, that is, the underlying set is allowed (in the extreme case) to be the empty set.

However, some treatments insist that $S \ne \O$.

It may be necessary to check which definition is being referred to in any given context.

Also see

 * Definition:Unitary Magma
 * Definition:Semigroup