ThmDex – An index of mathematical definitions, results, and conjectures.

Formulation F1772 on D264: Semigroup

F1772

Formulation 2

An D21: Algebraic structure $G = (X, f)$ is a semigroup if and only if

(1)	\begin{equation} \forall \, x, y \in X : f(x, y) \in X \end{equation}
(2)	\begin{equation} \forall \, x, y, z \in X : f(f(x, y), z) = f(x, f(y, z)) \end{equation}