\begin{definition}[Definition:Commutative Semigroup with respect to Equivalence Relation]
Let $C$ be a class.
Let $\thickapprox$ be an equivalence relation on $C$.
Let $\struct {C, \cdot}$ be a large magma.
Then $\struct {C, \cdot}$ is a '''commutative semigroup with respect to $\thickapprox$''' {{iff}}:
:it is a semigroup with respect to $\thickapprox$
:$\forall x, y \in C: x \cdot y \thickapprox y \cdot x$
\end{definition}