\begin{definition}[Definition:Semigroup]
Let $\struct {S, \circ}$ be a magma.
Then $\struct {S, \circ}$ is a '''semigroup''' {{iff}} $\circ$ is associative on $S$.
That is:
:A '''semigroup''' is an algebraic structure which is closed and whose operation is associative.
\end{definition}