In abstract algebra, a semigroup is an algebraic structure with a binary operation over its elements that is both closed and satisfies the associative property. So for semigroup *S* with generic operator •:

for all *a*, *b*, *c* in *S*, the equation (*a* • *b*) • *c* = *a* • (*b* • *c*) holds.

Again, closure also holds for this operation. So:

•: *S x S → S*

A semigroup can be thought of as an *associative* magma.

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