Magma

Magma is a basic kind of algebraic structure, consisting of a set equipped with a single binary operation which must be closed over the set.

A magma is a set M matched with an operation, •, that sends any two elements a,b ∈ M to another element, a • b ∈ M.

The symbol, •, is a general placeholder for a properly defined operation. To qualify as a magma, the set and operation (M, •) must satisfy the following requirement (known as the magma or closure axiom):

For all $a, b$ in $M$, the result of the operation $a \cdot b$ is also in $M$; in mathematical notation:

\display{a,b \in M \implies a \cdot b\in M}

If $\cdot$ is instead a partial operation, then $S$ is called a partial magma or more often a partial groupoid.