## 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