semigroup

Semigroup

context	$S$ … set
definiendum	$\langle\!\langle S,* \rangle\!\rangle \in$ semigroup(S)
inclusion	$\langle\!\langle S,* \rangle\!\rangle\in$ magma(S)
postulate	$(ab)c=a(bc)$

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.