Definition:Commutative Semigroup with respect to Equivalence Relation

Definition
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 $\thickapprox$ :
 * it is a semigroup with respect to $\thickapprox$
 * $\forall x, y \in C: x \cdot y \thickapprox y \cdot x$