Definition:Commutative Semigroup with respect to Equivalence Relation
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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 $\thickapprox$ if and only if:
- it is a semigroup with respect to $\thickapprox$
- $\forall x, y \in C: x \cdot y \thickapprox y \cdot x$
Sources
- 1981: Stanley Burris and H.P. Sankappanavar: A Course in Universal Algebra: $\text {II} \ \S 1$ Example $(2)$