| context | $S$ … set |
| definiendum | $\langle\!\langle S,* \rangle\!\rangle \in $ semigroup(S) |
| inclusion | $\langle\!\langle S,* \rangle\!\rangle\in $ magma(S) |
| postulate | $(a*b)*c=a*(b*c)$ |
The binary operation is often called multiplication.
The axioms $*\in \mathrm{binaryOp}(S)$ above means that a magma is closed with respect to the multiplication.
One generally calls $S$ the semigroup, i.e. the set where the operation “$*$” is defined on.
Wikipedia: Semigroup, Special classes of semigroups