Semigroup

Set

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

Discussion

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.

Reference

Wikipedia: Semigroup, Special classes of semigroups


Subset of

Magma